Area Moment of Inertia of specimen given bending moment and bending stress Calculator

✖The Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.ⓘ Bending Moment [M_b]			+10% -10%
✖Distance from Neutral Axis of Curved Beam is defined as the distance from an axis in the cross-section of a curved beam along which there are no longitudinal stresses or strains.ⓘ Distance from Neutral Axis of Curved Beam [y]			+10% -10%
✖Bending stress or allowable bending stress is the amount of bending stress that can be generated in a material before its failure or fracture.ⓘ Bending Stress [σ_b]			+10% -10%

✖Area Moment of Inertia is a property of a two-dimensional plane shape that characterizes its deflection under loading.ⓘ Area Moment of Inertia of specimen given bending moment and bending stress [I]

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Formula

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Area Moment of Inertia of specimen given bending moment and bending stress

Formula

`"I" = ("M"_{"b"}*"y")/"σ"_{"b"}`

Example

`"43875mm⁴"=("117000N*mm"*"21mm")/"56N/mm²"`

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Area Moment of Inertia of specimen given bending moment and bending stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress
I = (M_b*y)/σ_b
This formula uses 4 Variables

Variables Used

Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a property of a two-dimensional plane shape that characterizes its deflection under loading.
Bending Moment - (Measured in Newton Meter) - The Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend.
Distance from Neutral Axis of Curved Beam - (Measured in Meter) - Distance from Neutral Axis of Curved Beam is defined as the distance from an axis in the cross-section of a curved beam along which there are no longitudinal stresses or strains.
Bending Stress - (Measured in Pascal) - Bending stress or allowable bending stress is the amount of bending stress that can be generated in a material before its failure or fracture.

STEP 1: Convert Input(s) to Base Unit

Bending Moment: 117000 Newton Millimeter --> 117 Newton Meter (Check conversion here)
Distance from Neutral Axis of Curved Beam: 21 Millimeter --> 0.021 Meter (Check conversion here)
Bending Stress: 56 Newton per Square Millimeter --> 56000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I = (M_b*y)/σ_b --> (117*0.021)/56000000

Evaluating ... ...

I = 4.3875E-08

STEP 3: Convert Result to Output's Unit

4.3875E-08 Meter⁴ -->43875 Millimeter⁴ (Check conversion here)

FINAL ANSWER

43875 Millimeter⁴ <-- Area Moment of Inertia

(Calculation completed in 00.004 seconds)

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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Dayananda Sagar College of Engineering (DSCE), Bengaluru

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< 6 Stresses due to Bending Moment Calculators

Area Moment of Inertia of specimen given bending moment and bending stress

Go Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress

Bending stress in specimen due to bending moment

Go Bending Stress = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Area Moment of Inertia

Bending moment in specimen given bending stress

Go Bending Moment = (Bending Stress*Area Moment of Inertia)/Distance from Neutral Axis of Curved Beam

Area Moment of inertia of rectangular cross-section along centroidal axis parallel to breadth

Go Area Moment of Inertia = (Breadth of rectangular section*(Length of rectangular section^3))/12

Area Moment of inertia of rectangular cross-section along centroidal axis parallel to length

Go Area Moment of Inertia = ((Length of rectangular section^3)*Breadth of rectangular section)/12

Area Moment of Inertia of Circular Cross-Section about Diameter

Go Area Moment of Inertia = pi*(Diameter of circular section of shaft^4)/64

Area Moment of Inertia of specimen given bending moment and bending stress Formula

Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress
I = (M_b*y)/σ_b

What is bending stress?

The stress caused due to bending moment is called bending stress. One side of the neutral axis experiences compression and another extension.

How to Calculate Area Moment of Inertia of specimen given bending moment and bending stress?

Area Moment of Inertia of specimen given bending moment and bending stress calculator uses Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress to calculate the Area Moment of Inertia, Area Moment of Inertia of specimen given bending moment and bending stress formula is defined as the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation. Area Moment of Inertia is denoted by I symbol.

How to calculate Area Moment of Inertia of specimen given bending moment and bending stress using this online calculator? To use this online calculator for Area Moment of Inertia of specimen given bending moment and bending stress, enter Bending Moment (M_b), Distance from Neutral Axis of Curved Beam (y) & Bending Stress (σ_b) and hit the calculate button. Here is how the Area Moment of Inertia of specimen given bending moment and bending stress calculation can be explained with given input values -> 4.4E+16 = (117*0.021)/56000000.

FAQ

What is Area Moment of Inertia of specimen given bending moment and bending stress?

Area Moment of Inertia of specimen given bending moment and bending stress formula is defined as the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation and is represented as I = (M_b*y)/σ_b or Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress. The Bending Moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend, Distance from Neutral Axis of Curved Beam is defined as the distance from an axis in the cross-section of a curved beam along which there are no longitudinal stresses or strains & Bending stress or allowable bending stress is the amount of bending stress that can be generated in a material before its failure or fracture.

How to calculate Area Moment of Inertia of specimen given bending moment and bending stress?

Area Moment of Inertia of specimen given bending moment and bending stress formula is defined as the quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation is calculated using Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress. To calculate Area Moment of Inertia of specimen given bending moment and bending stress, you need Bending Moment (M_b), Distance from Neutral Axis of Curved Beam (y) & Bending Stress (σ_b). With our tool, you need to enter the respective value for Bending Moment, Distance from Neutral Axis of Curved Beam & Bending Stress 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 Area Moment of Inertia?

In this formula, Area Moment of Inertia uses Bending Moment, Distance from Neutral Axis of Curved Beam & Bending Stress. We can use 3 other way(s) to calculate the same, which is/are as follows -

Area Moment of Inertia = (Breadth of rectangular section*(Length of rectangular section^3))/12
Area Moment of Inertia = ((Length of rectangular section^3)*Breadth of rectangular section)/12
Area Moment of Inertia = pi*(Diameter of circular section of shaft^4)/64

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