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

✖Moment of resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress.ⓘ Moment of Resistance [M_resistance]			+10% -10%
✖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.ⓘ Radius of Neutral Layer [R]			+10% -10%
✖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.ⓘ Young's Modulus of Beam [E]			+10% -10%

✖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.ⓘ Moment of Inertia of Area of Section given Young's Modulus of Beam [I_circular]

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

STEP 0: Pre-Calculation Summary

Formula Used

MOI of Area of Circular Section = (Moment of Resistance*Radius of Neutral Layer)/Young's Modulus of Beam
I_circular = (M_resistance*R)/E
This formula uses 4 Variables

Variables Used

MOI of Area of Circular Section - (Measured in Meter⁴) - 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.
Moment of Resistance - (Measured in Newton Meter) - Moment of resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress.
Radius of Neutral Layer - (Measured in Meter) - 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.
Young's Modulus of Beam - (Measured in Pascal) - 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.

STEP 1: Convert Input(s) to Base Unit

Moment of Resistance: 7000 Newton Millimeter --> 7 Newton Meter (Check conversion here)
Radius of Neutral Layer: 2 Millimeter --> 0.002 Meter (Check conversion here)
Young's Modulus of Beam: 14 Megapascal --> 14000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_circular = (M_resistance*R)/E --> (7*0.002)/14000000

Evaluating ... ...

I_circular = 1E-09

STEP 3: Convert Result to Output's Unit

1E-09 Meter⁴ -->1000 Millimeter⁴ (Check conversion here)

FINAL ANSWER

1000 Millimeter⁴ <-- MOI of Area of Circular Section

(Calculation completed in 00.020 seconds)

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< Stress Variation Calculators

Radius of Neutral Axis using Moment of Resistance

LaTeX Go Radius of Neutral Layer = (Young's Modulus of Beam*MOI of Area of Circular Section)/Moment of Resistance

Distance between Neutral and Considered Layer using Moment of Resistance

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

Moment of Resistance using Stress in Layer of Beam

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

Stress in Layer of Beam given Moment of Resistance

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

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

LaTeX Go

MOI of Area of Circular Section = (Moment of Resistance*Radius of Neutral Layer)/Young's Modulus of Beam
I_circular = (M_resistance*R)/E

What is Moment of Inertia?

The Moment of Inertia (I), also known as the second moment of area, is a geometric property of a cross-section that quantifies its resistance to bending and torsion. It plays a crucial role in structural and mechanical engineering, particularly in analyzing beams and other load-bearing structures.

How to Calculate 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 calculator uses MOI of Area of Circular Section = (Moment of Resistance*Radius of Neutral Layer)/Young's Modulus of Beam to calculate 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 calculate Moment of Inertia of Area of Section given Young's Modulus of Beam using this online calculator? To use this online calculator 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. Here is how the Moment of Inertia of Area of Section given Young's Modulus of Beam calculation can be explained with given input values -> 1E+15 = (7*0.002)/14000000.

FAQ

What is Moment of Inertia of Area of Section given Young's Modulus of Beam?

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 and is represented as I_circular = (M_resistance*R)/E or MOI of Area of Circular Section = (Moment of Resistance*Radius of Neutral Layer)/Young's Modulus of Beam. Moment of resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress, 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 & 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.

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

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 is calculated using MOI of Area of Circular Section = (Moment of Resistance*Radius of Neutral Layer)/Young's Modulus of Beam. To calculate Moment of Inertia of Area of Section given Young's Modulus of Beam, you need Moment of Resistance (M_resistance), Radius of Neutral Layer (R) & Young's Modulus of Beam (E). With our tool, you need to enter the respective value for Moment of Resistance, Radius of Neutral Layer & Young's Modulus of Beam and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate MOI of Area of Circular Section?

In this formula, MOI of Area of Circular Section uses Moment of Resistance, Radius of Neutral Layer & Young's Modulus of Beam. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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