Nth Moment of Inertia Calculator

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Bending of Beams

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Nonlinear Behavior of Beams

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Yield Criteria

✖Breadth of rectangular beam is the width of the beam.ⓘ Breadth of rectangular beam [b]			+10% -10%
✖Depth of rectangular beam is the height of the beam.ⓘ Depth of rectangular beam [d]			+10% -10%
✖Material Constant is the constant used when the beam yielded plastically.ⓘ Material Constant [n]			+10% -10%

✖Nth Moment of Inertia is the integral arising from non-linear behavior of material.ⓘ Nth Moment of Inertia [I_n]

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Formula

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Nth Moment of Inertia

Formula

`"I"_{"n"} = ("b"*"d"^("n"+2))/(("n"+2)*2^("n"+1))`

Example

`"4.7E^17mm⁴"=("80mm"*("100mm")^("0.25"+2))/(("0.25"+2)*2^("0.25"+1))`

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Nth Moment of Inertia Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Moment of Inertia = (Breadth of rectangular beam*Depth of rectangular beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1))
I_n = (b*d^(n+2))/((n+2)*2^(n+1))
This formula uses 4 Variables

Variables Used

Nth Moment of Inertia - (Measured in Meter⁴) - Nth Moment of Inertia is the integral arising from non-linear behavior of material.
Breadth of rectangular beam - (Measured in Millimeter) - Breadth of rectangular beam is the width of the beam.
Depth of rectangular beam - (Measured in Millimeter) - Depth of rectangular beam is the height of the beam.
Material Constant - Material Constant is the constant used when the beam yielded plastically.

STEP 1: Convert Input(s) to Base Unit

Breadth of rectangular beam: 80 Millimeter --> 80 Millimeter No Conversion Required
Depth of rectangular beam: 100 Millimeter --> 100 Millimeter No Conversion Required
Material Constant: 0.25 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_n = (b*d^(n+2))/((n+2)*2^(n+1)) --> (80*100^(0.25+2))/((0.25+2)*2^(0.25+1))

Evaluating ... ...

I_n = 472737.413061777

STEP 3: Convert Result to Output's Unit

472737.413061777 Meter⁴ -->4.72737413061777E+17 Millimeter⁴ (Check conversion here)

FINAL ANSWER

4.72737413061777E+17 ≈ 4.7E+17 Millimeter⁴ <-- Nth Moment of Inertia

(Calculation completed in 00.004 seconds)

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< 4 Nonlinear Behavior of Beams Calculators

Radius of Curvature given Bending Stress

Go Radius of curvature = ((Elastoplastic Modulus*Depth Yielded Plastically^Material Constant)/Maximum Bending Stress in Plastic State)^(1/Material Constant)

Nth Moment of Inertia

Go Nth Moment of Inertia = (Breadth of rectangular beam*Depth of rectangular beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1))

Maximum Bending Stress in Plastic State

Go Maximum Bending Stress in Plastic State = (Maximum Bending Moment*Depth Yielded Plastically^Material Constant)/Nth Moment of Inertia

Radius of Curvature given Bending Moment

Go Radius of curvature = ((Elastoplastic Modulus*Nth Moment of Inertia )/Maximum Bending Moment)^(1/Material Constant)

Nth Moment of Inertia Formula

Nth Moment of Inertia = (Breadth of rectangular beam*Depth of rectangular beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1))
I_n = (b*d^(n+2))/((n+2)*2^(n+1))

What is Nth moment of inertia?

Nth moment of inertia is the integral arising from non-linear behavior of material. It is measured when the material is plastically deformed.

How to Calculate Nth Moment of Inertia?

Nth Moment of Inertia calculator uses Nth Moment of Inertia = (Breadth of rectangular beam*Depth of rectangular beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1)) to calculate the Nth Moment of Inertia, Nth Moment of Inertia is defined as the integral arising from non-linear behavior of material. Nth Moment of Inertia is denoted by I_n symbol.

How to calculate Nth Moment of Inertia using this online calculator? To use this online calculator for Nth Moment of Inertia, enter Breadth of rectangular beam (b), Depth of rectangular beam (d) & Material Constant (n) and hit the calculate button. Here is how the Nth Moment of Inertia calculation can be explained with given input values -> 4.7E+29 = (0.08*0.1^(0.25+2))/((0.25+2)*2^(0.25+1)).

FAQ

What is Nth Moment of Inertia?

Nth Moment of Inertia is defined as the integral arising from non-linear behavior of material and is represented as I_n = (b*d^(n+2))/((n+2)*2^(n+1)) or Nth Moment of Inertia = (Breadth of rectangular beam*Depth of rectangular beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1)). Breadth of rectangular beam is the width of the beam, Depth of rectangular beam is the height of the beam & Material Constant is the constant used when the beam yielded plastically.

How to calculate Nth Moment of Inertia?

Nth Moment of Inertia is defined as the integral arising from non-linear behavior of material is calculated using Nth Moment of Inertia = (Breadth of rectangular beam*Depth of rectangular beam^(Material Constant+2))/((Material Constant+2)*2^(Material Constant+1)). To calculate Nth Moment of Inertia, you need Breadth of rectangular beam (b), Depth of rectangular beam (d) & Material Constant (n). With our tool, you need to enter the respective value for Breadth of rectangular beam, Depth of rectangular beam & Material Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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