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Moment of Inertia of Area of Section given Young's Modulus of Beam Formula

GoMoment of Inertia of Area of Section of Beam given Stress in Layer Formula

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MOI of Area of Circular Section define its resistance to rotation or bending when subjected to external forces. A larger MOI means the structure will be more resistant to deformation. Check FAQs

I circular = \frac{M resistance \cdot R}{E}

I_circular - MOI of Area of Circular Section?M_resistance - Moment of Resistance?R - Radius of Neutral Layer?E - Young's Modulus of Beam?

Moment of Inertia of Area of Section given Young's Modulus of Beam Example

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Here is how the Moment of Inertia of Area of Section given Young's Modulus of Beam equation looks like with Values.

Here is how the Moment of Inertia of Area of Section given Young's Modulus of Beam equation looks like with Units.

Here is how the Moment of Inertia of Area of Section given Young's Modulus of Beam equation looks like.

1000 = \frac{7000 \cdot 2}{14}

1000mm⁴ = \frac{7000N*mm \cdot 2mm}{14MPa}

1000 = \frac{7000 \cdot 2}{14}

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Moment of Inertia of Area of Section given Young's Modulus of Beam Solution

Follow our step by step solution on how to calculate Moment of Inertia of Area of Section given Young's Modulus of Beam?

FIRST Step Consider the formula

I circular = \frac{M resistance \cdot R}{E}

Next Step Substitute values of Variables

∴

I circular = \frac{7000N*mm \cdot 2mm}{14MPa}

Next Step Convert Units

∴

I circular = \frac{7N*m \cdot 0.002m}{1.4E+7Pa}

Next Step Prepare to Evaluate

∴

I circular = \frac{7 \cdot 0.002}{1.4E+7}

Next Step Evaluate

∴

I circular = 1E-09m⁴

LAST Step Convert to Output's Unit

∴

I circular = 1000mm⁴

Moment of Inertia of Area of Section given Young's Modulus of Beam Formula Elements

Variables

MOI of Area of Circular Section

MOI of Area of Circular Section define its resistance to rotation or bending when subjected to external forces. A larger MOI means the structure will be more resistant to deformation.

Symbol: I_circular

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find MOI of Area of Circular Section

Moment of Resistance

Moment of resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress.

Symbol: M_resistance

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Moment of Resistance

Radius of Neutral Layer

Radius of Neutral Layer is the location within a material under bending where the stress is zero. The neutral layer lies between the compressive and tensile regions of the material.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Neutral Layer

Young's Modulus of Beam

Young's Modulus of Beam is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Young's Modulus of Beam

Other Formulas to find MOI of Area of Circular Section

Go Moment of Inertia of Area of Section of Beam given Stress in Layer

I circular = \frac{M resistance \cdot d nl}{σ}

Other formulas in Stress Variation category

Go Radius of Neutral Axis using Moment of Resistance

R = \frac{E \cdot I circular}{M resistance}

Go Moment of Resistance using Stress in Layer of Beam

M resistance = \frac{σ \cdot I circular}{d nl}

Go Stress in Layer of Beam given Moment of Resistance

σ = \frac{M resistance \cdot d nl}{I circular}

Go Distance between Neutral and Considered Layer using Moment of Resistance

d nl = \frac{σ \cdot I circular}{M resistance}

How to Evaluate Moment of Inertia of Area of Section given Young's Modulus of Beam?

Moment of Inertia of Area of Section given Young's Modulus of Beam evaluator uses MOI of Area of Circular Section = (Moment of Resistance*Radius of Neutral Layer)/Young's Modulus of Beam to evaluate the MOI of Area of Circular Section, The Moment of Inertia of Area of Section given Young's Modulus of Beam formula is defined as a measure of the resistance of a beam to bending stress, providing a way to calculate the beam's ability to resist deformation under external loads, taking into account the Young's modulus of the beam material. MOI of Area of Circular Section is denoted by I_circular symbol.

How to evaluate Moment of Inertia of Area of Section given Young's Modulus of Beam using this online evaluator? To use this online evaluator for Moment of Inertia of Area of Section given Young's Modulus of Beam, enter Moment of Resistance (M_resistance), Radius of Neutral Layer (R) & Young's Modulus of Beam (E) and hit the calculate button.

FAQs on Moment of Inertia of Area of Section given Young's Modulus of Beam

What is the formula to find Moment of Inertia of Area of Section given Young's Modulus of Beam?

The formula of Moment of Inertia of Area of Section given Young's Modulus of Beam is expressed as MOI of Area of Circular Section = (Moment of Resistance*Radius of Neutral Layer)/Young's Modulus of Beam. Here is an example- 1E+15 = (7*0.002)/14000000.

How to calculate Moment of Inertia of Area of Section given Young's Modulus of Beam?

With Moment of Resistance (M_resistance), Radius of Neutral Layer (R) & Young's Modulus of Beam (E) we can find Moment of Inertia of Area of Section given Young's Modulus of Beam using the formula - MOI of Area of Circular Section = (Moment of Resistance*Radius of Neutral Layer)/Young's Modulus of Beam.

What are the other ways to Calculate MOI of Area of Circular Section?

Here are the different ways to Calculate MOI of Area of Circular Section-

MOI of Area of Circular Section=(Moment of Resistance*Distance from Neutral Layer)/Stress in Layer

Can the Moment of Inertia of Area of Section given Young's Modulus of Beam be negative?

No, the Moment of Inertia of Area of Section given Young's Modulus of Beam, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia of Area of Section given Young's Modulus of Beam?

Moment of Inertia of Area of Section given Young's Modulus of 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 of Area of Section given Young's Modulus of Beam can be measured.

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Moment of Inertia of Area of Section given Young's Modulus of Beam Formula

​GoMoment of Inertia of Area of Section of Beam given Stress in Layer Formula

Moment of Inertia of Area of Section given Young's Modulus of Beam Example

Moment of Inertia of Area of Section given Young's Modulus of Beam Solution

Moment of Inertia of Area of Section given Young's Modulus of Beam Formula Elements

Other Formulas to find MOI of Area of Circular Section

Other formulas in Stress Variation category

How to Evaluate Moment of Inertia of Area of Section given Young's Modulus of Beam?

FAQs on Moment of Inertia of Area of Section given Young's Modulus of Beam

Variable Name

GoMoment of Inertia of Area of Section of Beam given Stress in Layer Formula