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

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

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

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Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis. Check FAQs

I = \frac{F s}{𝜏 beam \cdot b} \cdot (\frac{B}{8} \cdot (D^{2} - d^{2}) + \frac{b}{2} \cdot (\frac{d^{2}}{4} - y^{2}))

I - Moment of Inertia of Area of Section?F_s - Shear Force on Beam?𝜏_beam - Shear Stress in Beam?b - Thickness of Beam Web?B - Width of Beam Section?D - Outer Depth of I section?d - Inner Depth of I Section?y - Distance from Neutral Axis?

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

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Here is how the Moment of Inertia of I-Section given Shear Stress of Web equation looks like with Values.

Here is how the Moment of Inertia of I-Section given Shear Stress of Web equation looks like with Units.

Here is how the Moment of Inertia of I-Section given Shear Stress of Web equation looks like.

0.1154 = \frac{4.8}{6 \cdot 7} \cdot (\frac{100}{8} \cdot (9000^{2} - 450^{2}) + \frac{7}{2} \cdot (\frac{450^{2}}{4} - 5^{2}))

0.1154m⁴ = \frac{4.8kN}{6MPa \cdot 7mm} \cdot (\frac{100mm}{8} \cdot ({9000mm}^{2} - {450mm}^{2}) + \frac{7mm}{2} \cdot (\frac{{450mm}^{2}}{4} - {5mm}^{2}))

0.1154 = \frac{4.8}{6 \cdot 7} \cdot (\frac{100}{8} \cdot (9000^{2} - 450^{2}) + \frac{7}{2} \cdot (\frac{450^{2}}{4} - 5^{2}))

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Home » Physics » Mechanical » Strength of Materials » Moment of Inertia of I-Section given Shear Stress of Web

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

Follow our step by step solution on how to calculate Moment of Inertia of I-Section given Shear Stress of Web?

FIRST Step Consider the formula

I = \frac{F s}{𝜏 beam \cdot b} \cdot (\frac{B}{8} \cdot (D^{2} - d^{2}) + \frac{b}{2} \cdot (\frac{d^{2}}{4} - y^{2}))

Next Step Substitute values of Variables

∴

I = \frac{4.8kN}{6MPa \cdot 7mm} \cdot (\frac{100mm}{8} \cdot ({9000mm}^{2} - {450mm}^{2}) + \frac{7mm}{2} \cdot (\frac{{450mm}^{2}}{4} - {5mm}^{2}))

Next Step Convert Units

∴

I = \frac{4800N}{6E+6Pa \cdot 0.007m} \cdot (\frac{0.1m}{8} \cdot ({9m}^{2} - {0.45m}^{2}) + \frac{0.007m}{2} \cdot (\frac{{0.45m}^{2}}{4} - {0.005m}^{2}))

Next Step Prepare to Evaluate

∴

I = \frac{4800}{6E+6 \cdot 0.007} \cdot (\frac{0.1}{8} \cdot (9^{2} - {0.45}^{2}) + \frac{0.007}{2} \cdot (\frac{{0.45}^{2}}{4} - {0.005}^{2}))

Next Step Evaluate

∴

I = 0.11544524m⁴

LAST Step Rounding Answer

∴

I = 0.1154m⁴

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

Variables

Moment of Inertia of Area of Section

Moment of Inertia of Area of Section is the second moment of the area of the section about the neutral axis.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Shear Force on Beam

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

Symbol: F_s

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Shear Stress in Beam

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.

Symbol: 𝜏_beam

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Thickness of Beam Web

Thickness of Beam Web is the thickness of the vertical piece that connects the two flanges.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Width of Beam Section

Width of Beam Section is the width of the rectangular cross-section of the beam parallel to the axis in consideration.

Symbol: B

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Outer Depth of I section

The Outer Depth of I section is a measure of distance, the distance between the outer bars of the I-section.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Inner Depth of I Section

Inner Depth of I Section is a measure of distance, the distance between the inner bars of the I-section.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Distance from Neutral Axis

Distance from Neutral Axis is the distance of the considered layer from the neutral layer.

Symbol: y

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Formula and 2000+ more formulas!

Verified by Dipto Mandal

Indian Institute of Information Technology (IIIT), Guwahati

Dipto Mandal has verified this Formula and 400+ more formulas!

Other Formulas to find Moment of Inertia of Area of Section

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

I = \frac{F s \cdot B \cdot (D^{2} - d^{2})}{8 \cdot 𝜏 beam \cdot b}

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

I = \frac{F s}{𝜏 beam \cdot b} \cdot (\frac{B \cdot (D^{2} - d^{2})}{8} + \frac{b \cdot d^{2}}{8})

Other formulas in Shear Stress Distribution in Web category

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

b = \frac{F s \cdot B \cdot (D^{2} - d^{2})}{8 \cdot I \cdot 𝜏 beam}

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

B = \frac{𝜏 beam \cdot 8 \cdot I \cdot b}{F s \cdot (D^{2} - d^{2})}

How to Evaluate Moment of Inertia of I-Section given Shear Stress of Web?

Moment of Inertia of I-Section given Shear Stress of Web evaluator uses 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)) to evaluate the Moment of Inertia of Area of Section, The Moment of Inertia of I-Section given Shear Stress of Web formula is defined as a measure of the tendency of an I-section beam to resist changes in its rotational motion, considering the shear stress of the web, which is essential in structural analysis and design. Moment of Inertia of Area of Section is denoted by I symbol.

How to evaluate Moment of Inertia of I-Section given Shear Stress of Web using this online evaluator? To use this online evaluator for Moment of Inertia of I-Section given Shear Stress of Web, 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) & Distance from Neutral Axis (y) and hit the calculate button.

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

What is the formula to find Moment of Inertia of I-Section given Shear Stress of Web?

The formula of Moment of Inertia of I-Section given Shear Stress of Web is expressed as 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)). Here is an example- 0.115445 = 4800/(6000000*0.007)*(0.1/8*(9^2-0.45^2)+0.007/2*(0.45^2/4-0.005^2)).

How to calculate Moment of Inertia of I-Section given Shear Stress of Web?

With 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) & Distance from Neutral Axis (y) we can find Moment of Inertia of I-Section given Shear Stress of Web using the formula - 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)).

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

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

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

Can the Moment of Inertia of I-Section given Shear Stress of Web be negative?

No, the Moment of Inertia of I-Section given Shear Stress of Web, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia of I-Section given Shear Stress of Web?

Moment of Inertia of I-Section given Shear Stress of Web is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Moment of Inertia of I-Section given Shear Stress of Web can be measured.

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

​GoMoment of Inertia of Section given Shear Stress at Junction of Top of Web Formula

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

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

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

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

Credits

Other Formulas to find Moment of Inertia of Area of Section

Other formulas in Shear Stress Distribution in Web category

How to Evaluate Moment of Inertia of I-Section given Shear Stress of Web?

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

Variable Name

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

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