Moment of Inertia of Section for I-section Calculator

✖Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.ⓘ Shear Force on Beam [F_s]			+10% -10%
✖Shear Stress in Beam is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress in Beam [𝜏_beam]			+10% -10%
✖The Outer Depth of I section is a measure of distance, the distance between the outer bars of the I-section.ⓘ Outer Depth of I section [D]			+10% -10%
✖Distance from Neutral Axis is the distance of the considered layer from the neutral layer.ⓘ Distance from Neutral Axis [y]			+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 for I-section [I]

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Moment of Inertia of Section for I-section

Formula

`"I" = "F"_{"s"}/(2*"𝜏"_{"beam"})*(("D"^2)/2-"y"^2)`

Example

`"0.0162m⁴"="4.8kN"/(2*"6MPa")*((("9000mm")^2)/2-("5mm")^2)`

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Moment of Inertia of Section for I-section Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*((Outer Depth of I section^2)/2-Distance from Neutral Axis^2)
I = F_s/(2*𝜏_beam)*((D^2)/2-y^2)
This formula uses 5 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 on Beam - (Measured in Newton) - Shear Force on Beam is the force which causes shear deformation to occur in the shear plane.
Shear Stress in Beam - (Measured in Pascal) - Shear Stress in Beam is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
Outer Depth of I section - (Measured in Meter) - The Outer Depth of I section is a measure of distance, the distance between the outer bars of the I-section.
Distance from Neutral Axis - (Measured in Meter) - Distance from Neutral Axis is the distance of the considered layer from the neutral layer.

STEP 1: Convert Input(s) to Base Unit

Shear Force on Beam: 4.8 Kilonewton --> 4800 Newton (Check conversion here)
Shear Stress in Beam: 6 Megapascal --> 6000000 Pascal (Check conversion here)
Outer Depth of I section: 9000 Millimeter --> 9 Meter (Check conversion here)
Distance from Neutral Axis: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = F_s/(2*𝜏_beam)*((D^2)/2-y^2) --> 4800/(2*6000000)*((9^2)/2-0.005^2)

Evaluating ... ...

I = 0.01619999

STEP 3: Convert Result to Output's Unit

0.01619999 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.01619999 ≈ 0.0162 Meter⁴ <-- Moment of Inertia of Area of Section

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Shear Stress In Beam » Shear Stress Distribution for Different Sections » Shear Stress in I Section » Shear Stress Distribution in Flange » Moment of Inertia of Section for I-section

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< 15 Shear Stress Distribution in Flange Calculators

Distance of Considered Section from Neutral Axis given Shear Stress in Flange

Go Distance from Neutral Axis = sqrt((Outer Depth of I section^2)/2-(2*Moment of Inertia of Area of Section)/Shear Force on Beam*Shear Stress in Beam)

Outer Depth of I-section given Shear Stress in Flange

Go Outer Depth of I section = 4*sqrt((2*Moment of Inertia of Area of Section)/Shear Force on Beam*Shear Stress in Beam+Distance from Neutral Axis^2)

Inner Depth of I-section given Shear Stress in Lower Edge of Flange

Go Inner Depth of I Section = sqrt(Outer Depth of I section^2-(8*Moment of Inertia of Area of Section)/Shear Force on Beam*Shear Stress in Beam)

Outer Depth of I section given Shear Stress in Lower Edge of Flange

Go Outer Depth of I section = sqrt((8*Moment of Inertia of Area of Section)/Shear Force on Beam*Shear Stress in Beam+Inner Depth of I Section^2)

Moment of Inertia of Section for I-section

Go Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*((Outer Depth of I section^2)/2-Distance from Neutral Axis^2)

Shear Force in Flange of I-section

Go Shear Force on Beam = (2*Moment of Inertia of Area of Section*Shear Stress in Beam)/((Outer Depth of I section^2)/2-Distance from Neutral Axis^2)

Shear Stress in Flange of I-section

Go Shear Stress in Beam = Shear Force on Beam/(2*Moment of Inertia of Area of Section)*(Outer Depth of I section^2/2-Distance from Neutral Axis^2)

Moment of Inertia of I section given Shear Stress in Lower Edge of Flange

Go Moment of Inertia of Area of Section = Shear Force on Beam/(8*Shear Stress in Beam)*(Outer Depth of I section^2-Inner Depth of I Section^2)

Shear Stress in Lower Edge of Flange of I-section

Go Shear Stress in Beam = Shear Force on Beam/(8*Moment of Inertia of Area of Section)*(Outer Depth of I section^2-Inner Depth of I Section^2)

Shear Force in Lower Edge of Flange in I-section

Go Shear Force on Beam = (8*Moment of Inertia of Area of Section*Shear Stress in Beam)/(Outer Depth of I section^2-Inner Depth of I Section^2)

Width of Section given Area above Considered Section of Flange

Go Width of Beam Section = Area of Section above Considered Level/(Outer Depth of I section/2-Distance from Neutral Axis)

Area of Flange or Area above Considered Section

Go Area of Section above Considered Level = Width of Beam Section*(Outer Depth of I section/2-Distance from Neutral Axis)

Distance of CG of Considered Area of Flange from Neutral Axis in I Section

Go Distance of CG of Area from NA = 1/2*(Outer Depth of I section/2+Distance from Neutral Axis)

Distance of Lower Edge of Flange from Neutral Axis

Go Distance from Neutral Axis = Inner Depth of I Section/2

Distance of Upper Edge of Flange from Neutral Axis

Go Distance from Neutral Axis = Outer Depth of I section/2

Moment of Inertia of Section for I-section Formula

Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*((Outer Depth of I section^2)/2-Distance from Neutral Axis^2)
I = F_s/(2*𝜏_beam)*((D^2)/2-y^2)

Where is shear stress distribution in a beam section maximum?

The maximum shear stress occurs at the neutral axis and is zero at both the top and bottom surface of the beam. Shear flow has the units of force per unit distance.

How to Calculate Moment of Inertia of Section for I-section?

Moment of Inertia of Section for I-section calculator uses Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*((Outer Depth of I section^2)/2-Distance from Neutral Axis^2) to calculate the Moment of Inertia of Area of Section, The Moment of inertia of section for I-section formula is defined as a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. Moment of Inertia of Area of Section is denoted by I symbol.

How to calculate Moment of Inertia of Section for I-section using this online calculator? To use this online calculator for Moment of Inertia of Section for I-section, enter Shear Force on Beam (F_s), Shear Stress in Beam (𝜏_beam), Outer Depth of I section (D) & Distance from Neutral Axis (y) and hit the calculate button. Here is how the Moment of Inertia of Section for I-section calculation can be explained with given input values -> 0.0162 = 4800/(2*6000000)*((9^2)/2-0.005^2).

FAQ

What is Moment of Inertia of Section for I-section?

The Moment of inertia of section for I-section formula is defined as a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis and is represented as I = F_s/(2*𝜏_beam)*((D^2)/2-y^2) or Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*((Outer Depth of I section^2)/2-Distance from Neutral Axis^2). Shear Force on Beam is the force which causes shear deformation to occur in the shear plane, Shear Stress in Beam is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, The Outer Depth of I section is a measure of distance, the distance between the outer bars of the I-section & Distance from Neutral Axis is the distance of the considered layer from the neutral layer.

How to calculate Moment of Inertia of Section for I-section?

The Moment of inertia of section for I-section formula is defined as a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis is calculated using Moment of Inertia of Area of Section = Shear Force on Beam/(2*Shear Stress in Beam)*((Outer Depth of I section^2)/2-Distance from Neutral Axis^2). To calculate Moment of Inertia of Section for I-section, you need Shear Force on Beam (F_s), Shear Stress in Beam (𝜏_beam), Outer Depth of I section (D) & Distance from Neutral Axis (y). With our tool, you need to enter the respective value for Shear Force on Beam, Shear Stress in Beam, Outer Depth of I section & Distance from Neutral Axis and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Moment of Inertia of Area of Section?

In this formula, Moment of Inertia of Area of Section uses Shear Force on Beam, Shear Stress in Beam, Outer Depth of I section & Distance from Neutral Axis. We can use 1 other way(s) to calculate the same, which is/are as follows -

Moment of Inertia of Area of Section = Shear Force on Beam/(8*Shear Stress in Beam)*(Outer Depth of I section^2-Inner Depth of I Section^2)

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