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

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

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

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Area Moment of Inertia is a property of a two-dimensional plane shape that characterizes its deflection under loading. Check FAQs

I = \frac{M b \cdot y}{σ b}

I - Area Moment of Inertia?M_b - Bending Moment?y - Distance from Neutral Axis of Curved Beam?σ_b - Bending Stress?

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

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Here is how the Area Moment of Inertia of specimen given bending moment and bending stress equation looks like with Values.

Here is how the Area Moment of Inertia of specimen given bending moment and bending stress equation looks like with Units.

Here is how the Area Moment of Inertia of specimen given bending moment and bending stress equation looks like.

43875 = \frac{117000 \cdot 21}{56}

43875mm⁴ = \frac{117000N*mm \cdot 21mm}{56N/mm²}

43875 = \frac{117000 \cdot 21}{56}

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

Follow our step by step solution on how to calculate Area Moment of Inertia of specimen given bending moment and bending stress?

FIRST Step Consider the formula

I = \frac{M b \cdot y}{σ b}

Next Step Substitute values of Variables

∴

I = \frac{117000N*mm \cdot 21mm}{56N/mm²}

Next Step Convert Units

∴

I = \frac{117N*m \cdot 0.021m}{5.6E+7Pa}

Next Step Prepare to Evaluate

∴

I = \frac{117 \cdot 0.021}{5.6E+7}

Next Step Evaluate

∴

I = 4.3875E-08m⁴

LAST Step Convert to Output's Unit

∴

I = 43875mm⁴

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

Variables

Area Moment of Inertia

Area Moment of Inertia is a property of a two-dimensional plane shape that characterizes its deflection under loading.

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Bending Moment

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.

Symbol: M_b

Measurement: TorqueUnit: N*mm

Note: Value should be greater than 0.

Formulas to find Bending Moment

Distance from Neutral Axis of Curved Beam

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.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Neutral Axis of Curved Beam

Bending Stress

Bending stress or allowable bending stress is the amount of bending stress that can be generated in a material before its failure or fracture.

Symbol: σ_b

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Bending Stress

Other Formulas to find Area Moment of Inertia

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

I = \frac{b \cdot (L^{3})}{12}

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

I = \frac{(L^{3}) \cdot b}{12}

Go Area Moment of Inertia of Circular Cross-Section about Diameter

I = π \cdot \frac{{d c}^{4}}{64}

Other formulas in Stresses due to Bending Moment category

Go Bending stress in specimen due to bending moment

σ b = \frac{M b \cdot y}{I}

Go Bending moment in specimen given bending stress

M b = \frac{σ b \cdot I}{y}

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

Area Moment of Inertia of specimen given bending moment and bending stress evaluator uses Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress to evaluate 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 evaluate Area Moment of Inertia of specimen given bending moment and bending stress using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Area Moment of Inertia of specimen given bending moment and bending stress?

The formula of Area Moment of Inertia of specimen given bending moment and bending stress is expressed as Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress. Here is an example- 4.4E+16 = (117*0.021)/56000000.

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

With Bending Moment (M_b), Distance from Neutral Axis of Curved Beam (y) & Bending Stress (σ_b) we can find Area Moment of Inertia of specimen given bending moment and bending stress using the formula - Area Moment of Inertia = (Bending Moment*Distance from Neutral Axis of Curved Beam)/Bending Stress.

What are the other ways to Calculate Area Moment of Inertia?

Here are the different ways to Calculate Area Moment of Inertia-

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

Can the Area Moment of Inertia of specimen given bending moment and bending stress be negative?

No, the Area Moment of Inertia of specimen given bending moment and bending stress, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Area Moment of Inertia of specimen given bending moment and bending stress?

Area Moment of Inertia of specimen given bending moment and bending stress is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Area Moment of Inertia of specimen given bending moment and bending stress can be measured.

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

​GoArea Moment of inertia of rectangular cross-section along centroidal axis parallel to breadth Formula

​GoArea Moment of inertia of rectangular cross-section along centroidal axis parallel to length Formula

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

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

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

Other Formulas to find Area Moment of Inertia

Other formulas in Stresses due to Bending Moment category

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

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

Variable Name

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

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