Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam Calculator

✖Width of Flange is the dimension of the flange measured parallel to the neutral axis.ⓘ Width of Flange [b_f]			+10% -10%
✖Shear Force is the force which causes shear deformation to occur in the shear plane.ⓘ Shear Force [V]			+10% -10%
✖Width of Web (bw) is the effective width of the member for flanged section.ⓘ Width of Web [b_w]			+10% -10%
✖Overall Depth of I Beam is the total height or depth of the I-section from the top fiber of the top flange to the bottom fiber of the bottom flange.ⓘ Overall Depth of I Beam [D]			+10% -10%
✖Depth of Web is the dimension of the web measured perpendicular to the neutral axis.ⓘ Depth of Web [d_w]			+10% -10%
✖Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.ⓘ Maximum Shear Stress [τ_max]			+10% -10%

✖Area Moment of Inertia is a moment about the centroidal axis without considering mass.ⓘ Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam [I]

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Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area Moment of Inertia = (((Width of Flange*Shear Force)/(8*Width of Web))*(Overall Depth of I Beam^2-Depth of Web^2))/Maximum Shear Stress+((Shear Force*Depth of Web^2)/8)/Maximum Shear Stress
I = (((b_f*V)/(8*b_w))*(D^2-d_w^2))/τ_max+((V*d_w^2)/8)/τ_max
This formula uses 7 Variables

Variables Used

Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a moment about the centroidal axis without considering mass.
Width of Flange - (Measured in Meter) - Width of Flange is the dimension of the flange measured parallel to the neutral axis.
Shear Force - (Measured in Newton) - Shear Force is the force which causes shear deformation to occur in the shear plane.
Width of Web - (Measured in Meter) - Width of Web (bw) is the effective width of the member for flanged section.
Overall Depth of I Beam - (Measured in Meter) - Overall Depth of I Beam is the total height or depth of the I-section from the top fiber of the top flange to the bottom fiber of the bottom flange.
Depth of Web - (Measured in Meter) - Depth of Web is the dimension of the web measured perpendicular to the neutral axis.
Maximum Shear Stress - (Measured in Pascal) - Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

STEP 1: Convert Input(s) to Base Unit

Width of Flange: 250 Millimeter --> 0.25 Meter (Check conversion here)
Shear Force: 24.8 Kilonewton --> 24800 Newton (Check conversion here)
Width of Web: 0.04 Meter --> 0.04 Meter No Conversion Required
Overall Depth of I Beam: 800 Millimeter --> 0.8 Meter (Check conversion here)
Depth of Web: 15 Millimeter --> 0.015 Meter (Check conversion here)
Maximum Shear Stress: 42 Megapascal --> 42000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (((b_f*V)/(8*b_w))*(D^2-d_w^2))/τ_max+((V*d_w^2)/8)/τ_max --> (((0.25*24800)/(8*0.04))*(0.8^2-0.015^2))/42000000+((24800*0.015^2)/8)/42000000

Evaluating ... ...

I = 0.000295150907738095

STEP 3: Convert Result to Output's Unit

0.000295150907738095 Meter⁴ -->295150907.738095 Millimeter⁴ (Check conversion here)

FINAL ANSWER

295150907.738095 ≈ 3E+8 Millimeter⁴ <-- Area Moment of Inertia

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< I Beam Calculators

Moment of Inertia given Longitudinal Shear Stress in Web for I beam

LaTeX Go Area Moment of Inertia = ((Width of Flange*Shear Force)/(8*Shear Stress*Width of Web))*(Overall Depth of I Beam^2-Depth of Web^2)

Moment of Inertia given Longitudinal Shear Stress at lower edge in Flange of I beam

LaTeX Go Area Moment of Inertia = (Shear Force/(8*Shear Stress))*(Overall Depth of I Beam^2-Depth of Web^2)

Longitudinal Shear Stress in Flange at Lower Depth of I beam

LaTeX Go Shear Stress = (Shear Force/(8*Area Moment of Inertia))*(Overall Depth of I Beam^2-Depth of Web^2)

Transverse Shear given Longitudinal Shear Stress in Flange for I beam

LaTeX Go Shear Force = (8*Area Moment of Inertia*Shear Stress)/(Overall Depth of I Beam^2-Depth of Web^2)

Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam Formula

LaTeX Go

What is Longitudinal Shear Stress?

The Longitudinal Shear Stress in a beam occurs along the longitudinal axis and is visualized by a slip in the layers of the beam. In addition to the transverse shear force, a longitudinal shear force also exists in the beam. This load produces a shear stress called the longitudinal (or horizontal) shear stress.

How to Calculate Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam?

Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam calculator uses Area Moment of Inertia = (((Width of Flange*Shear Force)/(8*Width of Web))*(Overall Depth of I Beam^2-Depth of Web^2))/Maximum Shear Stress+((Shear Force*Depth of Web^2)/8)/Maximum Shear Stress to calculate the Area Moment of Inertia, The Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam is defined as area moment of inertia of cross-section undergoing shearing (unit- mm^4). Area Moment of Inertia is denoted by I symbol.

How to calculate Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam using this online calculator? To use this online calculator for Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam, enter Width of Flange (b_f), Shear Force (V), Width of Web (b_w), Overall Depth of I Beam (D), Depth of Web (d_w) & Maximum Shear Stress (τ_max) and hit the calculate button. Here is how the Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam calculation can be explained with given input values -> 0.000295 = (((0.25*24800)/(8*0.04))*(0.8^2-0.015^2))/42000000+((24800*0.015^2)/8)/42000000.

FAQ

What is Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam?

The Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam is defined as area moment of inertia of cross-section undergoing shearing (unit- mm^4) and is represented as I = (((b_f*V)/(8*b_w))*(D^2-d_w^2))/τ_max+((V*d_w^2)/8)/τ_max or Area Moment of Inertia = (((Width of Flange*Shear Force)/(8*Width of Web))*(Overall Depth of I Beam^2-Depth of Web^2))/Maximum Shear Stress+((Shear Force*Depth of Web^2)/8)/Maximum Shear Stress. Width of Flange is the dimension of the flange measured parallel to the neutral axis, Shear Force is the force which causes shear deformation to occur in the shear plane, Width of Web (bw) is the effective width of the member for flanged section, Overall Depth of I Beam is the total height or depth of the I-section from the top fiber of the top flange to the bottom fiber of the bottom flange, Depth of Web is the dimension of the web measured perpendicular to the neutral axis & Maximum Shear Stress is the greatest extent a shear force can be concentrated in a small area.

How to calculate Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam?

The Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam is defined as area moment of inertia of cross-section undergoing shearing (unit- mm^4) is calculated using Area Moment of Inertia = (((Width of Flange*Shear Force)/(8*Width of Web))*(Overall Depth of I Beam^2-Depth of Web^2))/Maximum Shear Stress+((Shear Force*Depth of Web^2)/8)/Maximum Shear Stress. To calculate Moment of Inertia given Maximum Longitudinal Shear Stress in Web for I beam, you need Width of Flange (b_f), Shear Force (V), Width of Web (b_w), Overall Depth of I Beam (D), Depth of Web (d_w) & Maximum Shear Stress (τ_max). With our tool, you need to enter the respective value for Width of Flange, Shear Force, Width of Web, Overall Depth of I Beam, Depth of Web & Maximum Shear Stress 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 Area Moment of Inertia?

In this formula, Area Moment of Inertia uses Width of Flange, Shear Force, Width of Web, Overall Depth of I Beam, Depth of Web & Maximum Shear Stress. We can use 2 other way(s) to calculate the same, which is/are as follows -

Area Moment of Inertia = (Shear Force/(8*Shear Stress))*(Overall Depth of I Beam^2-Depth of Web^2)
Area Moment of Inertia = ((Width of Flange*Shear Force)/(8*Shear Stress*Width of Web))*(Overall Depth of I Beam^2-Depth of Web^2)

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