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

GoNeutral Axis Moment of Inertia given Maximum Stress for Short Beams 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{y \cdot M r}{σ b}

I - Area Moment of Inertia?y - Distance from Neutral Axis?M_r - Moment of Resistance?σ_b - Bending Stress?

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

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Here is how the Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber equation looks like with Values.

Here is how the Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber equation looks like with Units.

Here is how the Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber equation looks like.

0.0016 = \frac{25 \cdot 4.608}{0.072}

0.0016m⁴ = \frac{25mm \cdot 4.608kN*m}{0.072MPa}

0.0016 = \frac{25 \cdot 4.608}{0.072}

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Strength of Materials » fx Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber

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

Follow our step by step solution on how to calculate Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber?

FIRST Step Consider the formula

I = \frac{y \cdot M r}{σ b}

Next Step Substitute values of Variables

∴

I = \frac{25mm \cdot 4.608kN*m}{0.072MPa}

Next Step Convert Units

∴

I = \frac{0.025m \cdot 4608N*m}{72000Pa}

Next Step Prepare to Evaluate

∴

I = \frac{0.025 \cdot 4608}{72000}

LAST Step Evaluate

∴

I = 0.0016m⁴

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

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

Moment of Resistance

Moment of Resistance is the couple produced by the internal forces in a beam subjected to bending under the maximum permissible stress.

Symbol: M_r

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Moment of Resistance

Bending Stress

Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

Symbol: σ_b

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Bending Stress

Other Formulas to find Area Moment of Inertia

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

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

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

Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber evaluator uses Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress to evaluate the Area Moment of Inertia, The Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber formula is defined as moment of inertia of the material when the cross section is undergoing simple bending. Area Moment of Inertia is denoted by I symbol.

How to evaluate Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber using this online evaluator? To use this online evaluator for Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber, enter Distance from Neutral Axis (y), Moment of Resistance (M_r) & Bending Stress (σ_b) and hit the calculate button.

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

What is the formula to find Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber?

The formula of Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber is expressed as Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/Bending Stress. Here is an example- 0.0016 = (0.025*4608)/72000.

How to calculate Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber?

With Distance from Neutral Axis (y), Moment of Resistance (M_r) & Bending Stress (σ_b) we can find Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber using the formula - Area Moment of Inertia = (Distance from Neutral Axis*Moment of Resistance)/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=(Maximum Bending Moment*Cross Sectional Area*Distance from Neutral Axis)/((Maximum Stress*Cross Sectional Area)-(Axial Load))
Area Moment of Inertia=(Moment of Resistance*Radius of Curvature)/Young's Modulus

Can the Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber be negative?

No, the Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber?

Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber is usually measured using the Meter⁴[m⁴] for Second Moment of Area. Centimeter⁴[m⁴], Millimeter⁴[m⁴] are the few other units in which Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber can be measured.

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

​GoNeutral Axis Moment of Inertia given Maximum Stress for Short Beams Formula

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

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

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

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

Other Formulas to find Area Moment of Inertia

Other formulas in Combined Axial and Bending Loads category

How to Evaluate Moment of Inertia given Moment of Resistance, Stress induced and Distance from Extreme Fiber?

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

Variable Name

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

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