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Moment of Inertia of Circular Section given Shear Stress Formula

GoMoment of Inertia of Circular Section given Maximum Shear Stress Formula

GoMoment of Inertia of Circular Section Formula

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Moment of Inertia of Area of Section is a geometric property that quantifies how a cross-sectional area is distributed relative to an axis. Check FAQs

I = \frac{F s \cdot \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}}{𝜏 beam \cdot B}

I - Moment of Inertia of Area of Section?F_s - Shear Force on Beam?r - Radius of Circular Section?y - Distance from Neutral Axis?𝜏_beam - Shear Stress in Beam?B - Width of Beam Section?

Moment of Inertia of Circular Section given Shear Stress Example

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

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

Here is how the Moment of Inertia of Circular Section given Shear Stress equation looks like.

0.0092 = \frac{4.8 \cdot \frac{2}{3} \cdot {(1200^{2} - 5^{2})}^{\frac{3}{2}}}{6 \cdot 100}

0.0092m⁴ = \frac{4.8kN \cdot \frac{2}{3} \cdot {({1200mm}^{2} - {5mm}^{2})}^{\frac{3}{2}}}{6MPa \cdot 100mm}

0.0092 = \frac{4.8 \cdot \frac{2}{3} \cdot {(1200^{2} - 5^{2})}^{\frac{3}{2}}}{6 \cdot 100}

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Moment of Inertia of Circular Section given Shear Stress Solution

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

FIRST Step Consider the formula

I = \frac{F s \cdot \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}}{𝜏 beam \cdot B}

Next Step Substitute values of Variables

∴

I = \frac{4.8kN \cdot \frac{2}{3} \cdot {({1200mm}^{2} - {5mm}^{2})}^{\frac{3}{2}}}{6MPa \cdot 100mm}

Next Step Convert Units

∴

I = \frac{4800N \cdot \frac{2}{3} \cdot {({1.2m}^{2} - {0.005m}^{2})}^{\frac{3}{2}}}{6E+6Pa \cdot 0.1m}

Next Step Prepare to Evaluate

∴

I = \frac{4800 \cdot \frac{2}{3} \cdot {({1.2}^{2} - {0.005}^{2})}^{\frac{3}{2}}}{6E+6 \cdot 0.1}

Next Step Evaluate

∴

I = 0.00921576000104167m⁴

LAST Step Rounding Answer

∴

I = 0.0092m⁴

Moment of Inertia of Circular Section given Shear Stress Formula Elements

Variables

Moment of Inertia of Area of Section

Moment of Inertia of Area of Section is a geometric property that quantifies how a cross-sectional area is distributed relative to an axis.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Area of Section

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.

Formulas to find Shear Force on Beam

Radius of Circular Section

Radius of Circular Section is the distance from the center of a circle to any point on its boundary, it represent the characteristic size of a circular cross-section in various applications.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Circular Section

Distance from Neutral Axis

Distance from Neutral Axis is the perpendicular distance from a point in an element to the neutral axis, it is the line where element experiences no stress when the beam is subjected to bending.

Symbol: y

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Distance from Neutral Axis

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.

Formulas to find Shear Stress in Beam

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.

Formulas to find Width of Beam Section

Other Formulas to find Moment of Inertia of Area of Section

Go Moment of Inertia of Circular Section given Maximum Shear Stress

I = \frac{F s}{3 \cdot 𝜏 max} \cdot r^{2}

Go Moment of Inertia of Circular Section

I = \frac{π}{4} \cdot r^{4}

Other formulas in Moment of Inertia category

Go Area Moment of Considered Area about Neutral Axis

A y = \frac{2}{3} \cdot {(r^{2} - y^{2})}^{\frac{3}{2}}

How to Evaluate Moment of Inertia of Circular Section given Shear Stress?

Moment of Inertia of Circular Section given Shear Stress evaluator uses Moment of Inertia of Area of Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section) to evaluate the Moment of Inertia of Area of Section, The Moment of Inertia of Circular Section given Shear Stress formula is defined as a measure of the tendency of an object to resist changes in its rotational motion, calculated in terms of shear stress, radius, and beam width, providing insights into the structural integrity of circular sections under stress. Moment of Inertia of Area of Section is denoted by I symbol.

How to evaluate Moment of Inertia of Circular Section given Shear Stress using this online evaluator? To use this online evaluator for Moment of Inertia of Circular Section given Shear Stress, enter Shear Force on Beam (F_s), Radius of Circular Section (r), Distance from Neutral Axis (y), Shear Stress in Beam (𝜏_beam) & Width of Beam Section (B) and hit the calculate button.

FAQs on Moment of Inertia of Circular Section given Shear Stress

What is the formula to find Moment of Inertia of Circular Section given Shear Stress?

The formula of Moment of Inertia of Circular Section given Shear Stress is expressed as Moment of Inertia of Area of Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section). Here is an example- 0.009216 = (4800*2/3*(1.2^2-0.005^2)^(3/2))/(6000000*0.1).

How to calculate Moment of Inertia of Circular Section given Shear Stress?

With Shear Force on Beam (F_s), Radius of Circular Section (r), Distance from Neutral Axis (y), Shear Stress in Beam (𝜏_beam) & Width of Beam Section (B) we can find Moment of Inertia of Circular Section given Shear Stress using the formula - Moment of Inertia of Area of Section = (Shear Force on Beam*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section).

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/(3*Maximum Shear Stress on Beam)*Radius of Circular Section^2
Moment of Inertia of Area of Section=pi/4*Radius of Circular Section^4

Can the Moment of Inertia of Circular Section given Shear Stress be negative?

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

Which unit is used to measure Moment of Inertia of Circular Section given Shear Stress?

Moment of Inertia of Circular Section given Shear Stress 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 Circular Section given Shear Stress can be measured.

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Moment of Inertia of Circular Section given Shear Stress Formula

​GoMoment of Inertia of Circular Section given Maximum Shear Stress Formula

​GoMoment of Inertia of Circular Section Formula

Moment of Inertia of Circular Section given Shear Stress Example

Moment of Inertia of Circular Section given Shear Stress Solution

Moment of Inertia of Circular Section given Shear Stress Formula Elements

Other Formulas to find Moment of Inertia of Area of Section

Other formulas in Moment of Inertia category

How to Evaluate Moment of Inertia of Circular Section given Shear Stress?

FAQs on Moment of Inertia of Circular Section given Shear Stress

Variable Name

GoMoment of Inertia of Circular Section given Maximum Shear Stress Formula

GoMoment of Inertia of Circular Section Formula