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

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

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

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Area Moment of Inertia is a moment about the centroidal axis without considering mass. Check FAQs

I = (\frac{b f \cdot V}{8 \cdot τ \cdot b w}) \cdot (D^{2} - {d w}^{2})

I - Area Moment of Inertia?b_f - Width of Flange?V - Shear Force?τ - Shear Stress?b_w - Width of Web?D - Overall Depth of I Beam?d_w - Depth of Web?

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

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Here is how the Moment of Inertia given Longitudinal Shear Stress in Web for I beam equation looks like with Values.

Here is how the Moment of Inertia given Longitudinal Shear Stress in Web for I beam equation looks like with Units.

Here is how the Moment of Inertia given Longitudinal Shear Stress in Web for I beam equation looks like.

2.3E+8 = (\frac{250 \cdot 24.8}{8 \cdot 55 \cdot 0.04}) \cdot (800^{2} - 15^{2})

2.3E+8mm⁴ = (\frac{250mm \cdot 24.8kN}{8 \cdot 55MPa \cdot 0.04m}) \cdot ({800mm}^{2} - {15mm}^{2})

2.3E+8 = (\frac{250 \cdot 24.8}{8 \cdot 55 \cdot 0.04}) \cdot (800^{2} - 15^{2})

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

Follow our step by step solution on how to calculate Moment of Inertia given Longitudinal Shear Stress in Web for I beam?

FIRST Step Consider the formula

I = (\frac{b f \cdot V}{8 \cdot τ \cdot b w}) \cdot (D^{2} - {d w}^{2})

Next Step Substitute values of Variables

∴

I = (\frac{250mm \cdot 24.8kN}{8 \cdot 55MPa \cdot 0.04m}) \cdot ({800mm}^{2} - {15mm}^{2})

Next Step Convert Units

∴

I = (\frac{0.25m \cdot 24800N}{8 \cdot 5.5E+7Pa \cdot 0.04m}) \cdot ({0.8m}^{2} - {0.015m}^{2})

Next Step Prepare to Evaluate

∴

I = (\frac{0.25 \cdot 24800}{8 \cdot 5.5E+7 \cdot 0.04}) \cdot ({0.8}^{2} - {0.015}^{2})

Next Step Evaluate

∴

I = 0.000225375284090909m⁴

Next Step Convert to Output's Unit

∴

I = 225375284.090909mm⁴

LAST Step Rounding Answer

∴

I = 2.3E+8mm⁴

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

Variables

Area Moment of Inertia

Area Moment of Inertia is a moment about the centroidal axis without considering mass.

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Width of Flange

Width of Flange is the dimension of the flange measured parallel to the neutral axis.

Symbol: b_f

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Flange

Shear Force

Shear Force is the force which causes shear deformation to occur in the shear plane.

Symbol: V

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Shear Force

Shear Stress

Shear Stress, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: τ

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress

Width of Web

Width of Web (bw) is the effective width of the member for flanged section.

Symbol: b_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Width of Web

Overall Depth of I Beam

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.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Overall Depth of I Beam

Depth of Web

Depth of Web is the dimension of the web measured perpendicular to the neutral axis.

Symbol: d_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Depth of Web

Other Formulas to find Area Moment of Inertia

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

I = (\frac{V}{8 \cdot τ}) \cdot (D^{2} - {d w}^{2})

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

I = \frac{(\frac{b f \cdot V}{8 \cdot b w}) \cdot (D^{2} - {d w}^{2})}{τ max} + \frac{\frac{V \cdot {d w}^{2}}{8}}{τ max}

Other formulas in I Beam category

Go Longitudinal Shear Stress in Flange at Lower Depth of I beam

τ = (\frac{V}{8 \cdot I}) \cdot (D^{2} - {d w}^{2})

Go Transverse Shear given Longitudinal Shear Stress in Flange for I beam

V = \frac{8 \cdot I \cdot τ}{D^{2} - {d w}^{2}}

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

Moment of Inertia given Longitudinal Shear Stress in Web for I beam evaluator uses 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) to evaluate the Area Moment of Inertia, Moment of Inertia given Longitudinal Shear Stress in Web for I beam is defined as the moment of inertia of the cross-section undergoing shearing. Area Moment of Inertia is denoted by I symbol.

How to evaluate Moment of Inertia given Longitudinal Shear Stress in Web for I beam using this online evaluator? To use this online evaluator for Moment of Inertia given Longitudinal Shear Stress in Web for I beam, enter Width of Flange (b_f), Shear Force (V), Shear Stress (τ), Width of Web (b_w), Overall Depth of I Beam (D) & Depth of Web (d_w) and hit the calculate button.

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

What is the formula to find Moment of Inertia given Longitudinal Shear Stress in Web for I beam?

The formula of Moment of Inertia given Longitudinal Shear Stress in Web for I beam is expressed as 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). Here is an example- 0.000225 = ((0.25*24800)/(8*55000000*0.04))*(0.8^2-0.015^2).

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

With Width of Flange (b_f), Shear Force (V), Shear Stress (τ), Width of Web (b_w), Overall Depth of I Beam (D) & Depth of Web (d_w) we can find Moment of Inertia given Longitudinal Shear Stress in Web for I beam using the formula - 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).

What are the other ways to Calculate Area Moment of Inertia?

Here are the different ways to Calculate Area Moment of Inertia-

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*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

Can the Moment of Inertia given Longitudinal Shear Stress in Web for I beam be negative?

No, the Moment of Inertia given Longitudinal Shear Stress in Web for I beam, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia given Longitudinal Shear Stress in Web for I beam?

Moment of Inertia given Longitudinal Shear Stress in Web for I beam is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Moment of Inertia given Longitudinal Shear Stress in Web for I beam can be measured.

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

​GoMoment of Inertia given Longitudinal Shear Stress at lower edge in Flange of I beam Formula

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

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

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

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

Other Formulas to find Area Moment of Inertia

Other formulas in I Beam category

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

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

Variable Name

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

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