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Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Formula

GoMoment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber Formula

GoMoment of Inertia given Young's Modulus, Moment of Resistance and Radius Formula

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Area Moment of Inertia is a property of a two-dimensional plane shape where it shows how its points are dispersed in an arbitrary axis in the cross-sectional plane. Check FAQs

I = \frac{M max \cdot A \cdot y}{(σ max \cdot A) - (P)}

I - Area Moment of Inertia?M_max - Maximum Bending Moment?A - Cross Sectional Area?y - Distance from Neutral Axis?σ_max - Maximum Stress?P - Axial Load?

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Example

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Here is how the Neutral Axis Moment of Inertia given Maximum Stress for Short Beams equation looks like with Values.

Here is how the Neutral Axis Moment of Inertia given Maximum Stress for Short Beams equation looks like with Units.

Here is how the Neutral Axis Moment of Inertia given Maximum Stress for Short Beams equation looks like.

0.0016 = \frac{7.7 \cdot 0.12 \cdot 25}{(0.137 \cdot 0.12) - (2000)}

0.0016m⁴ = \frac{7.7kN*m \cdot 0.12m² \cdot 25mm}{(0.137MPa \cdot 0.12m²) - (2000N)}

0.0016 = \frac{7.7 \cdot 0.12 \cdot 25}{(0.137 \cdot 0.12) - (2000)}

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Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Solution

Follow our step by step solution on how to calculate Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

FIRST Step Consider the formula

I = \frac{M max \cdot A \cdot y}{(σ max \cdot A) - (P)}

Next Step Substitute values of Variables

∴

I = \frac{7.7kN*m \cdot 0.12m² \cdot 25mm}{(0.137MPa \cdot 0.12m²) - (2000N)}

Next Step Convert Units

∴

I = \frac{7700N*m \cdot 0.12m² \cdot 0.025m}{(136979Pa \cdot 0.12m²) - (2000N)}

Next Step Prepare to Evaluate

∴

I = \frac{7700 \cdot 0.12 \cdot 0.025}{(136979 \cdot 0.12) - (2000)}

Next Step Evaluate

∴

I = 0.00160000221645329m⁴

LAST Step Rounding Answer

∴

I = 0.0016m⁴

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Formula Elements

Variables

Area Moment of Inertia

Area Moment of Inertia is a property of a two-dimensional plane shape where it shows how its points are dispersed in an arbitrary axis in the cross-sectional plane.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Maximum Bending Moment

Maximum Bending Moment occurs where shear force is zero.

Symbol: M_max

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment

Cross Sectional Area

The Cross Sectional Area is the breadth times the depth of the beam structure.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area

Distance from Neutral Axis

Distance from Neutral Axis is measured between N.A. and the extreme point.

Symbol: y

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Neutral Axis

Maximum Stress

Maximum Stress is the maximum amount of stress the taken by the beam/column before it breaks.

Symbol: σ_max

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Stress

Axial Load

Axial Load is a force applied on a structure directly along an axis of the structure.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Axial Load

Other Formulas to find Area Moment of Inertia

Go Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber

I = \frac{y \cdot M r}{σ b}

Go Moment of Inertia given Young's Modulus, Moment of Resistance and Radius

I = \frac{M r \cdot R curvature}{E}

Other formulas in Combined Axial and Bending Loads category

Go Maximum Stress for Short Beams

σ max = (\frac{P}{A}) + (\frac{M max \cdot y}{I})

Go Axial Load given Maximum Stress for Short Beams

P = A \cdot (σ max - (\frac{M max \cdot y}{I}))

Go Cross-Sectional Area given Maximum Stress for Short Beams

A = \frac{P}{σ max - (\frac{M max \cdot y}{I})}

Go Maximum Bending Moment given Maximum Stress for Short Beams

M max = \frac{(σ max - (\frac{P}{A})) \cdot I}{y}

How to Evaluate Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams evaluator uses Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load)) to evaluate the Area Moment of Inertia, The Neutral Axis Moment of Inertia given Maximum Stress for Short Beams formula is defined as a measure of the resistance of a body to angular acceleration about a given axis. Area Moment of Inertia is denoted by I symbol.

How to evaluate Neutral Axis Moment of Inertia given Maximum Stress for Short Beams using this online evaluator? To use this online evaluator for Neutral Axis Moment of Inertia given Maximum Stress for Short Beams, enter Maximum Bending Moment (M_max), Cross Sectional Area (A), Distance from Neutral Axis (y), Maximum Stress (σ_max) & Axial Load (P) and hit the calculate button.

FAQs on Neutral Axis Moment of Inertia given Maximum Stress for Short Beams

What is the formula to find Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

The formula of Neutral Axis Moment of Inertia given Maximum Stress for Short Beams is expressed as Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load)). Here is an example- 0.0016 = (7700*0.12*0.025)/((136979*0.12)-(2000)).

How to calculate Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

With Maximum Bending Moment (M_max), Cross Sectional Area (A), Distance from Neutral Axis (y), Maximum Stress (σ_max) & Axial Load (P) we can find Neutral Axis Moment of Inertia given Maximum Stress for Short Beams using the formula - Area Moment of Inertia = (Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load)).

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=(Distance from Neutral Axis*Moment of Resistance)/Bending Stress
Area Moment of Inertia=(Moment of Resistance*Radius of Curvature)/Young's Modulus

Can the Neutral Axis Moment of Inertia given Maximum Stress for Short Beams be negative?

No, the Neutral Axis Moment of Inertia given Maximum Stress for Short Beams, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Neutral Axis Moment of Inertia given Maximum Stress for Short Beams can be measured.

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Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Formula

​GoMoment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber Formula

​GoMoment of Inertia given Young's Modulus, Moment of Resistance and Radius Formula

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Example

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Solution

Neutral Axis Moment of Inertia given Maximum Stress for Short Beams Formula Elements

Other Formulas to find Area Moment of Inertia

Other formulas in Combined Axial and Bending Loads category

How to Evaluate Neutral Axis Moment of Inertia given Maximum Stress for Short Beams?

FAQs on Neutral Axis Moment of Inertia given Maximum Stress for Short Beams

Variable Name

GoMoment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber Formula

GoMoment of Inertia given Young's Modulus, Moment of Resistance and Radius Formula