Moment of Inertia of I-Section given Maximum Shear Stress and Force 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%
✖Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.ⓘ Thickness of Beam Web [b]			+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%

✖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 I-Section given Maximum Shear Stress and Force [I]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
I = F_s/(𝜏_beam*b)*((B*(D^2-d^2))/8+(b*d^2)/8)
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.
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.
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.

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)
Thickness of Beam Web: 7 Millimeter --> 0.007 Meter (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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

I = 0.11544525

STEP 3: Convert Result to Output's Unit

0.11544525 Meter⁴ --> No Conversion Required

FINAL ANSWER

0.11544525 ≈ 0.115445 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 Distribution in Web Calculators

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

LaTeX 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

LaTeX 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

LaTeX 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 Force at Junction of Top of Web

LaTeX 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))

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

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What is Maximum Shear Stress?

Maximum shear stress is the highest intensity of shear stress that occurs in a structural member when subjected to external loads. Understanding and calculating this stress is essential in engineering design, particularly for beams and other structural elements, to ensure they can safely withstand applied forces without failing.

How to Calculate Moment of Inertia of I-Section given Maximum Shear Stress and Force?

Moment of Inertia of I-Section given Maximum Shear Stress and Force calculator uses 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) to calculate the Moment of Inertia of Area of Section, The Moment of Inertia of I-Section given Maximum Shear Stress and Force formula is defined as a measure of the tendency of an I-section beam to resist changes in its rotation, calculated based on the maximum shear stress and force acting on the beam, providing a critical parameter in structural analysis and design. Moment of Inertia of Area of Section is denoted by I symbol.

How to calculate Moment of Inertia of I-Section given Maximum Shear Stress and Force using this online calculator? To use this online calculator for Moment of Inertia of I-Section given Maximum Shear Stress and Force, enter Shear Force on Beam (F_s), Shear Stress in Beam (𝜏_beam), Thickness of Beam Web (b), Width of Beam Section (B), Outer Depth of I section (D) & Inner Depth of I Section (d) and hit the calculate button. Here is how the Moment of Inertia of I-Section given Maximum Shear Stress and Force calculation can be explained with given input values -> 0.115445 = 4800/(6000000*0.007)*((0.1*(9^2-0.45^2))/8+(0.007*0.45^2)/8).

FAQ

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

The Moment of Inertia of I-Section given Maximum Shear Stress and Force formula is defined as a measure of the tendency of an I-section beam to resist changes in its rotation, calculated based on the maximum shear stress and force acting on the beam, providing a critical parameter in structural analysis and design and is represented as I = F_s/(𝜏_beam*b)*((B*(D^2-d^2))/8+(b*d^2)/8) or 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). 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, Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges, 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.

How to calculate Moment of Inertia of I-Section given Maximum Shear Stress and Force?

The Moment of Inertia of I-Section given Maximum Shear Stress and Force formula is defined as a measure of the tendency of an I-section beam to resist changes in its rotation, calculated based on the maximum shear stress and force acting on the beam, providing a critical parameter in structural analysis and design is calculated using 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). To calculate Moment of Inertia of I-Section given Maximum Shear Stress and Force, you need Shear Force on Beam (F_s), Shear Stress in Beam (𝜏_beam), Thickness of Beam Web (b), Width of Beam Section (B), Outer Depth of I section (D) & Inner Depth of I Section (d). With our tool, you need to enter the respective value for Shear Force on Beam, Shear Stress in Beam, Thickness of Beam Web, Width of Beam Section, Outer Depth of I section & Inner Depth of I Section 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, Thickness of Beam Web, Width of Beam Section, Outer Depth of I section & Inner Depth of I Section. We can use 3 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/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)

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