Moment of Inertia of Section given Shear Stress at Junction of Top of Web 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%
✖Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.ⓘ Width of Beam Section [B]			+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%
✖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%
✖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%
✖Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.ⓘ Thickness of Beam Web [b]			+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 given Shear Stress at Junction of Top of Web [I]

⎘ Copy

👎

Formula

✖

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

Formula

`"I" = ("F"_{"s"}*"B"*("D"^2-"d"^2))/(8*"𝜏"_{"beam"}*"b")`

Example

`"0.115425m⁴"=("4.8kN"*"100mm"*(("9000mm")^2-("450mm")^2))/(8*"6MPa"*"7mm")`

Calculator

LaTeX

Reset

👍

Download Shear Stress in I Section Formulas PDF PDF Image

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
I = (F_s*B*(D^2-d^2))/(8*𝜏_beam*b)
This formula uses 7 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.
Width of Beam Section - (Measured in Meter) - Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.
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.
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.
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.
Thickness of Beam Web - (Measured in Meter) - Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.

STEP 1: Convert Input(s) to Base Unit

Shear Force on Beam: 4.8 Kilonewton --> 4800 Newton (Check conversion here)
Width of Beam Section: 100 Millimeter --> 0.1 Meter (Check conversion here)
Outer Depth of I section: 9000 Millimeter --> 9 Meter (Check conversion here)
Inner Depth of I Section: 450 Millimeter --> 0.45 Meter (Check conversion here)
Shear Stress in Beam: 6 Megapascal --> 6000000 Pascal (Check conversion here)
Thickness of Beam Web: 7 Millimeter --> 0.007 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (F_s*B*(D^2-d^2))/(8*𝜏_beam*b) --> (4800*0.1*(9^2-0.45^2))/(8*6000000*0.007)

Evaluating ... ...

I = 0.115425

STEP 3: Convert Result to Output's Unit

0.115425 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.115425 Meter⁴ <-- Moment of Inertia of Area of Section

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Shear Stress In Beam » Shear Stress Distribution for Different Sections » Shear Stress in I Section » Shear Stress Distribution in Web » Moment of Inertia of Section given Shear Stress at Junction of Top of Web

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has verified this Calculator and 400+ more calculators!

< 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 Inertia of Section given Shear Stress at Junction of Top of Web Formula

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

Moment of Inertia of Section given Shear Stress at Junction of Top of Web calculator uses 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) to calculate the Moment of Inertia of Area of Section, The Moment of Inertia of Section given Shear Stress at Junction of Top of Web 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 given Shear Stress at Junction of Top of Web using this online calculator? To use this online calculator for Moment of Inertia of Section given Shear Stress at Junction of Top of Web, enter Shear Force on Beam (F_s), Width of Beam Section (B), Outer Depth of I section (D), Inner Depth of I Section (d), Shear Stress in Beam (𝜏_beam) & Thickness of Beam Web (b) and hit the calculate button. Here is how the Moment of Inertia of Section given Shear Stress at Junction of Top of Web calculation can be explained with given input values -> 0.115425 = (4800*0.1*(9^2-0.45^2))/(8*6000000*0.007).

FAQ

What is Moment of Inertia of Section given Shear Stress at Junction of Top of Web?

The Moment of Inertia of Section given Shear Stress at Junction of Top of Web 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*B*(D^2-d^2))/(8*𝜏_beam*b) or 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). Shear Force on Beam is the force which causes shear deformation to occur in the shear plane, Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration, The Outer Depth of I section is a measure of distance, the distance between the outer bars of the I-section, Inner Depth of I Section is a measure of distance, the distance between the inner bars of the I-section, 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 & Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.

How to calculate Moment of Inertia of Section given Shear Stress at Junction of Top of Web?

The Moment of Inertia of Section given Shear Stress at Junction of Top of Web 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*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). To calculate Moment of Inertia of Section given Shear Stress at Junction of Top of Web, you need Shear Force on Beam (F_s), Width of Beam Section (B), Outer Depth of I section (D), Inner Depth of I Section (d), Shear Stress in Beam (𝜏_beam) & Thickness of Beam Web (b). With our tool, you need to enter the respective value for Shear Force on Beam, Width of Beam Section, Outer Depth of I section, Inner Depth of I Section, Shear Stress in Beam & Thickness of Beam Web 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, Width of Beam Section, Outer Depth of I section, Inner Depth of I Section, Shear Stress in Beam & Thickness of Beam Web. 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/(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 = 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

Home

FREE PDFs

🔍 Search