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Moment of Inertia given Longitudinal Shear Stress Formula

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Area Moment of Inertia is a moment about the centroidal axis without considering mass. Check FAQs

I = \frac{V \cdot A \cdot y}{τ \cdot b}

I - Area Moment of Inertia?V - Shear Force?A - Cross Sectional Area?y - Distance from Neutral Axis?τ - Shear Stress?b - Breadth of Rectangular Section?

Moment of Inertia given Longitudinal Shear Stress Example

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Here is how the Moment of Inertia given Longitudinal Shear Stress equation looks like with Values.

Here is how the Moment of Inertia given Longitudinal Shear Stress equation looks like with Units.

Here is how the Moment of Inertia given Longitudinal Shear Stress equation looks like.

0.0001 = \frac{24.8 \cdot 3.2 \cdot 25}{55 \cdot 300}

0.0001mm⁴ = \frac{24.8kN \cdot 3.2m² \cdot 25mm}{55MPa \cdot 300mm}

0.0001 = \frac{24.8 \cdot 3.2 \cdot 25}{55 \cdot 300}

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Moment of Inertia given Longitudinal Shear Stress Solution

Follow our step by step solution on how to calculate Moment of Inertia given Longitudinal Shear Stress?

FIRST Step Consider the formula

I = \frac{V \cdot A \cdot y}{τ \cdot b}

Next Step Substitute values of Variables

∴

I = \frac{24.8kN \cdot 3.2m² \cdot 25mm}{55MPa \cdot 300mm}

Next Step Convert Units

∴

I = \frac{24800N \cdot 3.2m² \cdot 0.025m}{5.5E+7Pa \cdot 0.3m}

Next Step Prepare to Evaluate

∴

I = \frac{24800 \cdot 3.2 \cdot 0.025}{5.5E+7 \cdot 0.3}

Next Step Evaluate

∴

I = 1.20242424242424E-16m⁴

Next Step Convert to Output's Unit

∴

I = 0.000120242424242424mm⁴

LAST Step Rounding Answer

∴

I = 0.0001mm⁴

Moment of Inertia given Longitudinal Shear Stress Formula Elements

Variables

Area Moment of Inertia

Area Moment of Inertia is a moment about the centroidal axis without considering mass.

Symbol: I

Measurement: Second Moment of AreaUnit: mm⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Shear Force

Shear Force is the force which causes shear deformation to occur in the shear plane.

Symbol: V

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Shear Force

Cross Sectional Area

The cross sectional area is the breadth times the depth of the 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

Shear Stress

Shear Stress, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: τ

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress

Breadth of Rectangular Section

The Breadth of Rectangular Section is the distance or measurement from side to side of the section.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Breadth of Rectangular Section

Other formulas in Longitudinal Shear Stress category

Go Area given Longitudinal Shear Stress

A = \frac{τ \cdot I \cdot b}{V \cdot y}

Go Breadth for given Longitudinal Shear Stress

b = \frac{V \cdot A \cdot y}{I \cdot τ}

Go Maximum Distance from Neutral Axis to Extreme Fiber given Longitudinal Shear Stress

y = \frac{τ \cdot I \cdot b}{V \cdot A}

How to Evaluate Moment of Inertia given Longitudinal Shear Stress?

Moment of Inertia given Longitudinal Shear Stress evaluator uses Area Moment of Inertia = (Shear Force*Cross Sectional Area*Distance from Neutral Axis)/(Shear Stress*Breadth of Rectangular Section) to evaluate the Area Moment of Inertia, The Moment of Inertia given Longitudinal Shear Stress is defined as the moment of inertia of the cross-section which is undergoing the shear. Area Moment of Inertia is denoted by I symbol.

How to evaluate Moment of Inertia given Longitudinal Shear Stress using this online evaluator? To use this online evaluator for Moment of Inertia given Longitudinal Shear Stress, enter Shear Force (V), Cross Sectional Area (A), Distance from Neutral Axis (y), Shear Stress (τ) & Breadth of Rectangular Section (b) and hit the calculate button.

FAQs on Moment of Inertia given Longitudinal Shear Stress

What is the formula to find Moment of Inertia given Longitudinal Shear Stress?

The formula of Moment of Inertia given Longitudinal Shear Stress is expressed as Area Moment of Inertia = (Shear Force*Cross Sectional Area*Distance from Neutral Axis)/(Shear Stress*Breadth of Rectangular Section). Here is an example- 0.00012 = (24800*3.2*0.025)/(55000000*0.3).

How to calculate Moment of Inertia given Longitudinal Shear Stress?

With Shear Force (V), Cross Sectional Area (A), Distance from Neutral Axis (y), Shear Stress (τ) & Breadth of Rectangular Section (b) we can find Moment of Inertia given Longitudinal Shear Stress using the formula - Area Moment of Inertia = (Shear Force*Cross Sectional Area*Distance from Neutral Axis)/(Shear Stress*Breadth of Rectangular Section).

Can the Moment of Inertia given Longitudinal Shear Stress be negative?

No, the Moment of Inertia given Longitudinal Shear Stress, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia given Longitudinal Shear Stress?

Moment of Inertia given Longitudinal Shear Stress is usually measured using the Millimeter⁴[mm⁴] for Second Moment of Area. Meter⁴[mm⁴], Centimeter⁴[mm⁴] are the few other units in which Moment of Inertia given Longitudinal Shear Stress can be measured.

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Moment of Inertia given Longitudinal Shear Stress Formula

Moment of Inertia given Longitudinal Shear Stress Example

Moment of Inertia given Longitudinal Shear Stress Solution

Moment of Inertia given Longitudinal Shear Stress Formula Elements

Other formulas in Longitudinal Shear Stress category

How to Evaluate Moment of Inertia given Longitudinal Shear Stress?

FAQs on Moment of Inertia given Longitudinal Shear Stress

Variable Name