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Moment of Inertia of Circular Section given Maximum Shear Stress Formula

GoMoment of Inertia of Circular Section given 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}{3 \cdot 𝜏 max} \cdot r^{2}

I - Moment of Inertia of Area of Section?F_s - Shear Force on Beam?𝜏_max - Maximum Shear Stress on Beam?r - Radius of Circular Section?

Moment of Inertia of Circular Section given Maximum Shear Stress Example

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

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

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

0.0002 = \frac{4.8}{3 \cdot 11} \cdot 1200^{2}

0.0002m⁴ = \frac{4.8kN}{3 \cdot 11MPa} \cdot {1200mm}^{2}

0.0002 = \frac{4.8}{3 \cdot 11} \cdot 1200^{2}

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Moment of Inertia of Circular Section given Maximum Shear Stress Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

I = \frac{4.8kN}{3 \cdot 11MPa} \cdot {1200mm}^{2}

Next Step Convert Units

∴

I = \frac{4800N}{3 \cdot 1.1E+7Pa} \cdot {1.2m}^{2}

Next Step Prepare to Evaluate

∴

I = \frac{4800}{3 \cdot 1.1E+7} \cdot {1.2}^{2}

Next Step Evaluate

∴

I = 0.000209454545454545m⁴

LAST Step Rounding Answer

∴

I = 0.0002m⁴

Moment of Inertia of Circular Section given Maximum 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

Maximum Shear Stress on Beam

Maximum Shear Stress on Beam is the highest value of shear stress that occurs at any point within the beam when subjected to external loading, such as transverse forces.

Symbol: 𝜏_max

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Maximum Shear Stress 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

Other Formulas to find Moment of Inertia of Area of Section

Go Moment of Inertia of Circular Section given Shear Stress

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

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 Maximum Shear Stress?

Moment of Inertia of Circular Section given Maximum Shear Stress evaluator uses Moment of Inertia of Area of Section = Shear Force on Beam/(3*Maximum Shear Stress on Beam)*Radius of Circular Section^2 to evaluate the Moment of Inertia of Area of Section, The Moment of Inertia of Circular Section given Maximum Shear Stress formula is defined as a measure of the tendency of an object to resist changes in its rotational motion, specifically in a circular section where the maximum shear stress is a critical factor in determining the object's stability and structural integrity. Moment of Inertia of Area of Section is denoted by I symbol.

How to evaluate Moment of Inertia of Circular Section given Maximum Shear Stress using this online evaluator? To use this online evaluator for Moment of Inertia of Circular Section given Maximum Shear Stress, enter Shear Force on Beam (F_s), Maximum Shear Stress on Beam (𝜏_max) & Radius of Circular Section (r) and hit the calculate button.

FAQs on Moment of Inertia of Circular Section given Maximum Shear Stress

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

The formula of Moment of Inertia of Circular Section given Maximum Shear Stress is expressed as Moment of Inertia of Area of Section = Shear Force on Beam/(3*Maximum Shear Stress on Beam)*Radius of Circular Section^2. Here is an example- 0.000209 = 4800/(3*11000000)*1.2^2.

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

With Shear Force on Beam (F_s), Maximum Shear Stress on Beam (𝜏_max) & Radius of Circular Section (r) we can find Moment of Inertia of Circular Section given Maximum Shear Stress using the formula - Moment of Inertia of Area of Section = Shear Force on Beam/(3*Maximum Shear Stress on Beam)*Radius of Circular Section^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*2/3*(Radius of Circular Section^2-Distance from Neutral Axis^2)^(3/2))/(Shear Stress in Beam*Width of Beam Section)
Moment of Inertia of Area of Section=pi/4*Radius of Circular Section^4

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

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

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

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

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