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

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Stress Variation

Section Modulus

Section Modulus for Various Beams or Shape Sections

✖Moment of resistance is defined as 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%
✖The radius of neutral layer is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.ⓘ 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 is the second moment of the area of the section about the neutral axis.ⓘ Moment of Inertia of Area of Section given Young's Modulus of Beam [I_circular]

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Formula

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

Formula

`"I"_{"circular"} = ("M"_{"resistance"}*"R")/"E"`

Example

`"1000mm⁴"=("7000N*mm"*"2mm")/"14MPa"`

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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 is the second moment of the area of the section about the neutral axis.
Moment of Resistance - (Measured in Newton Meter) - Moment of resistance is defined as 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) - The radius of neutral layer is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
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 00.004 seconds)

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< 18 Stress Variation Calculators

Distance between Neutral and Considered Layer in Beam

Go Distance from neutral layer = (Stress in Layer*Radius of neutral layer)/(Young's Modulus of Beam*Area of Layer)

Force on Layer at Distance from Neutral Layer of Beam

Go Force on layer = ((Young's Modulus of Beam*Distance from neutral layer*Area of Layer)/Radius of neutral layer)

Young's Modulus of Beam given Force on Layer

Go Young's Modulus of Beam = (Force on layer*Radius of neutral layer)/(Distance from neutral layer*Area of Layer)

Radius of Neutral Layer given Force on Considered Layer

Go Radius of neutral layer = (Young's Modulus of Beam*Distance from neutral layer*Area of Layer)/Force on layer

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

Go MOI of Area of Circular Section = (Moment of Resistance*Radius of neutral layer)/Young's Modulus of Beam

Young's Modulus of Beam using Moment of Resistance

Go Young's Modulus of Beam = (Moment of Resistance*Radius of neutral layer)/MOI of Area of Circular Section

Radius of Neutral Axis using Moment of Resistance

Go Radius of neutral layer = (Young's Modulus of Beam*MOI of Area of Circular Section)/Moment of Resistance

Moment of Resistance

Go Moment of Resistance = (Young's Modulus of Beam*MOI of Area of Circular Section)/Radius of neutral layer

Distance between Neutral and Considered Layer using Moment of Resistance

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

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

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

Moment of Resistance using Stress in Layer of Beam

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

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

Stress in Layer Considering that Beam is Subjected to Simple Bending

Go Stress in Layer = (Young's Modulus of Beam*Distance from neutral layer)/Radius of neutral layer

Distance between Neutral and Considered Layers in Beams

Go Distance from neutral layer = (Stress in Layer*Radius of neutral layer)/Young's Modulus of Beam

Young's Modulus of Beam

Go Young's Modulus of Beam = (Stress in Layer*Radius of neutral layer)/Distance from neutral layer

Radius of Neutral Layer

Go Radius of neutral layer = (Young's Modulus of Beam*Distance from neutral layer)/Stress in Layer

Force on Layer of Beams given Stress in Layer

Go Force on layer = Stress in Layer*Area of Layer

Stress in Layer of Beam given Force on Layer

Go Stress in Layer = Force on layer/Area of Layer

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

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 meant by bending stress?

Bending stress is the normal stress that an object encounters when it is subjected to a large load at a particular point that causes the object to bend and become fatigued. Bending stress occurs when operating industrial equipment and in concrete and metallic structures when they are subjected to a tensile load.

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, Moment of Inertia of Area of Section given Young's Modulus of Beam formula is defined as a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. 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?

Moment of Inertia of Area of Section given Young's Modulus of Beam formula is defined as a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis 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 defined as the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress, The radius of neutral layer is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length & 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?

Moment of Inertia of Area of Section given Young's Modulus of Beam formula is defined as a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis 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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