Nth Moment of Inertia Calculator

✖Breadth of Rectangular Beam is the horizontal distance of a rectangular beam's cross-section, perpendicular to its length, in bending beam applications.ⓘ Breadth of Rectangular Beam [b]			+10% -10%
✖Depth of Rectangular Beam is the vertical distance from the neutral axis to the bottom of the beam, used to calculate bending stresses and moments.ⓘ Depth of Rectangular Beam [d]			+10% -10%
✖Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.ⓘ Material Constant [n]			+10% -10%

✖Nth Moment of Inertia is a measure of the distribution of the beam's mass around its axis of rotation, used in bending beam analysis.ⓘ Nth Moment of Inertia [I_n]

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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 Kilogram Square Meter) - Nth Moment of Inertia is a measure of the distribution of the beam's mass around its axis of rotation, used in bending beam analysis.
Breadth of Rectangular Beam - (Measured in Millimeter) - Breadth of Rectangular Beam is the horizontal distance of a rectangular beam's cross-section, perpendicular to its length, in bending beam applications.
Depth of Rectangular Beam - (Measured in Millimeter) - Depth of Rectangular Beam is the vertical distance from the neutral axis to the bottom of the beam, used to calculate bending stresses and moments.
Material Constant - Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.

STEP 1: Convert Input(s) to Base Unit

Breadth of Rectangular Beam: 80 Millimeter --> 80 Millimeter No Conversion Required
Depth of Rectangular Beam: 20 Millimeter --> 20 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*20^(0.25+2))/((0.25+2)*2^(0.25+1))

Evaluating ... ...

I_n = 12645.5424713879

STEP 3: Convert Result to Output's Unit

12645.5424713879 Kilogram Square Meter -->12645542471.3879 Kilogram Square Millimeter (Check conversion here)

FINAL ANSWER

12645542471.3879 ≈ 1.3E+10 Kilogram Square Millimeter <-- Nth Moment of Inertia

(Calculation completed in 00.004 seconds)

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< Nonlinear Behavior of Beams Calculators

Radius of Curvature given Bending Stress

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

Nth Moment of Inertia

LaTeX 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

LaTeX 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

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

Nth Moment of Inertia Formula

LaTeX Go

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 Moment of Inertia?

Moment of Inertia (I) is a property of a cross-section that quantifies its resistance to bending or rotational deformation. In the context of beams and structural elements, it reflects how the area is distributed relative to an axis, affecting the structure’s stiffness and ability to resist bending. A larger moment of inertia indicates that more of the area is positioned farther from the neutral axis, making the section more resistant to bending. This property is critical in engineering and design, as it helps determine the load-carrying capacity and deflection behavior of beams, ensuring structural stability and performance under applied loads.

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 formula is defined as a measure of the distribution of the beam's section modulus around its neutral axis, providing a way to calculate the beam's resistance to bending and deformation under various loads and stresses in structural analysis. 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 -> 1.3E+16 = (0.08*0.02^(0.25+2))/((0.25+2)*2^(0.25+1)).

FAQ

What is Nth Moment of Inertia?

Nth Moment of Inertia formula is defined as a measure of the distribution of the beam's section modulus around its neutral axis, providing a way to calculate the beam's resistance to bending and deformation under various loads and stresses in structural analysis 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 horizontal distance of a rectangular beam's cross-section, perpendicular to its length, in bending beam applications, Depth of Rectangular Beam is the vertical distance from the neutral axis to the bottom of the beam, used to calculate bending stresses and moments & Material Constant is a measure of the stiffness of a material, used to calculate the bending stress and deflection of beams under various loads.

How to calculate Nth Moment of Inertia?

Nth Moment of Inertia formula is defined as a measure of the distribution of the beam's section modulus around its neutral axis, providing a way to calculate the beam's resistance to bending and deformation under various loads and stresses in structural analysis 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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