Moment of Shaded Area of Web about Neutral Axis Calculator

✖Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.ⓘ Thickness of Beam Web [b]			+10% -10%
✖Inner Depth of I Section is a measure of distance, the distance between the inner bars of the I-section.ⓘ Inner 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 Shaded Area of Web about Neutral Axis [I]

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Formula

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Moment of Shaded Area of Web about Neutral Axis

Formula

`"I" = "b"/2*("d"^2/4-"y"^2)`

Example

`"0.000177m⁴"="7mm"/2*(("450mm")^2/4-("5mm")^2)`

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Download Shear Stress in I Section Formulas PDF

Moment of Shaded Area of Web about Neutral Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment of Inertia of Area of Section = Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2)
I = b/2*(d^2/4-y^2)
This formula uses 4 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.
Thickness of Beam Web - (Measured in Meter) - Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.
Inner Depth of I Section - (Measured in Meter) - Inner Depth of I Section is a measure of distance, the distance between the inner 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

Thickness of Beam Web: 7 Millimeter --> 0.007 Meter (Check conversion here)
Inner Depth of I Section: 450 Millimeter --> 0.45 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 = b/2*(d^2/4-y^2) --> 0.007/2*(0.45^2/4-0.005^2)

Evaluating ... ...

I = 0.0001771

STEP 3: Convert Result to Output's Unit

0.0001771 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.0001771 ≈ 0.000177 Meter⁴ <-- Moment of Inertia of Area of Section

(Calculation completed in 00.004 seconds)

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< 18 Shear Stress Distribution in Web Calculators

Shear Force in Web

Go Shear Force on Beam = (Moment of Inertia of Area of Section*Thickness of Beam Web*Shear Stress in Beam)/((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2))

Moment of Inertia of I-Section given Shear Stress of Web

Go Moment of Inertia of Area of Section = Shear Force on Beam/(Shear Stress in Beam*Thickness of Beam Web)*(Width of Beam Section/8*(Outer Depth of I section^2-Inner Depth of I Section^2)+Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2))

Shear Stress in Web

Go Shear Stress in Beam = Shear Force on Beam/(Moment of Inertia of Area of Section*Thickness of Beam Web)*(Width of Beam Section/8*(Outer Depth of I section^2-Inner Depth of I Section^2)+Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2))

Thickness of Web given Shear Stress of Web

Go Thickness of Beam Web = (Shear Force on Beam*Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/(8* Moment of Inertia of Area of Section*Shear Stress in Beam-Shear Force on Beam*(Inner Depth of I Section^2-4*Distance from Neutral Axis^2))

Maximum Shear Stress in I Section

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

Maximum Shear Force in I Section

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

Moment of Inertia of I-Section given Maximum Shear Stress and Force

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

Thickness of Web given Maximum Shear Stress and Force

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

Moment of Inertia of Section given Shear Stress at Junction of Top of Web

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

Thickness of Web given Shear Stress at Junction of Top of Web

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

Width of Section given Shear Stress at Junction of Top of Web

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

Shear Stress at Junction of Top of Web

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

Shear Force at Junction of Top of Web

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

Thickness of Web

Go Thickness of Beam Web = (2*Moment of Inertia of Area of Section)/((Inner Depth of I Section^2)/4-Distance from Neutral Axis^2)

Moment of Shaded Area of Web about Neutral Axis

Go Moment of Inertia of Area of Section = Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2)

Width of Section given Moment of Flange Area about Neutral Axis

Go Width of Beam Section = (8*Moment of Inertia of Area of Section)/(Outer Depth of I section^2-Inner Depth of I Section^2)

Moment of Flange Area about Neutral Axis

Go Moment of Inertia of Area of Section = (Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8

Distance of Considered Level from Neutral Axis at Junction of Top of Web

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

Moment of Shaded Area of Web about Neutral Axis Formula

Moment of Inertia of Area of Section = Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2)
I = b/2*(d^2/4-y^2)

Why shear stress is maximum at neutral axis?

The maximum shear stress is located at the neutral axis. As the point moves further from the neutral axis, the value of the shear stress is reduced until it reaches zero at both extremes. On the other hand, if the member is subjected to an axial load, shear stress varies with rotating the element.

How to Calculate Moment of Shaded Area of Web about Neutral Axis?

Moment of Shaded Area of Web about Neutral Axis calculator uses Moment of Inertia of Area of Section = Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2) to calculate the Moment of Inertia of Area of Section, The Moment of Shaded Area of Web about Neutral Axis 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 Shaded Area of Web about Neutral Axis using this online calculator? To use this online calculator for Moment of Shaded Area of Web about Neutral Axis, enter Thickness of Beam Web (b), Inner Depth of I Section (d) & Distance from Neutral Axis (y) and hit the calculate button. Here is how the Moment of Shaded Area of Web about Neutral Axis calculation can be explained with given input values -> 0.000177 = 0.007/2*(0.45^2/4-0.005^2).

FAQ

What is Moment of Shaded Area of Web about Neutral Axis?

The Moment of Shaded Area of Web about Neutral Axis 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 = b/2*(d^2/4-y^2) or Moment of Inertia of Area of Section = Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2). Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges, Inner Depth of I Section is a measure of distance, the distance between the inner 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 Shaded Area of Web about Neutral Axis?

The Moment of Shaded Area of Web about Neutral Axis 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 = Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2). To calculate Moment of Shaded Area of Web about Neutral Axis, you need Thickness of Beam Web (b), Inner Depth of I Section (d) & Distance from Neutral Axis (y). With our tool, you need to enter the respective value for Thickness of Beam Web, Inner 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 Thickness of Beam Web, Inner Depth of I Section & Distance from Neutral Axis. We can use 4 other way(s) to calculate the same, which is/are as follows -

Moment of Inertia of Area of Section = (Shear Force on Beam*Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/(8*Shear Stress in Beam*Thickness of Beam Web)
Moment of Inertia of Area of Section = Shear Force on Beam/(Shear Stress in Beam*Thickness of Beam Web)*((Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8+(Thickness of Beam Web*Inner Depth of I Section^2)/8)
Moment of Inertia of Area of Section = Shear Force on Beam/(Shear Stress in Beam*Thickness of Beam Web)*(Width of Beam Section/8*(Outer Depth of I section^2-Inner Depth of I Section^2)+Thickness of Beam Web/2*(Inner Depth of I Section^2/4-Distance from Neutral Axis^2))
Moment of Inertia of Area of Section = (Width of Beam Section*(Outer Depth of I section^2-Inner Depth of I Section^2))/8

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