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Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load Formula

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Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis. Check FAQs

I = (M \cdot \frac{c}{(σb max - (\frac{P axial}{A sectional}))})

I - Moment of Inertia?M - Maximum Bending Moment In Column?c - Distance from Neutral Axis to Extreme Point?σb^max - Maximum Bending Stress?P_axial - Axial Thrust?A_sectional - Cross Sectional Area?

Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load Example

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Here is how the Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load equation looks like with Values.

Here is how the Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load equation looks like with Units.

Here is how the Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load equation looks like.

8.0043 = (16 \cdot \frac{10}{(2 - (\frac{1500}{1.4}))})

8.0043cm⁴ = (16N*m \cdot \frac{10mm}{(2MPa - (\frac{1500N}{1.4m²}))})

8.0043 = (16 \cdot \frac{10}{(2 - (\frac{1500}{1.4}))})

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Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load?

FIRST Step Consider the formula

I = (M \cdot \frac{c}{(σb max - (\frac{P axial}{A sectional}))})

Next Step Substitute values of Variables

∴

I = (16N*m \cdot \frac{10mm}{(2MPa - (\frac{1500N}{1.4m²}))})

Next Step Convert Units

∴

I = (16N*m \cdot \frac{0.01m}{(2E+6Pa - (\frac{1500N}{1.4m²}))})

Next Step Prepare to Evaluate

∴

I = (16 \cdot \frac{0.01}{(2E+6 - (\frac{1500}{1.4}))})

Next Step Evaluate

∴

I = 8.0042880114347E-08m⁴

Next Step Convert to Output's Unit

∴

I = 8.0042880114347cm⁴

LAST Step Rounding Answer

∴

I = 8.0043cm⁴

Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load Formula Elements

Variables

Moment of Inertia

Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

Symbol: I

Measurement: Second Moment of AreaUnit: cm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

Maximum Bending Moment In Column

Maximum Bending Moment In Column is the highest amount of bending force that a column experiences due to applied loads, either axial or eccentric.

Symbol: M

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Maximum Bending Moment In Column

Distance from Neutral Axis to Extreme Point

Distance from Neutral Axis to Extreme Point is the distance between the neutral axis and the extreme point.

Symbol: c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Neutral Axis to Extreme Point

Maximum Bending Stress

Maximum Bending Stress is the highest stress experienced by a material subjected to a bending load.

Symbol: σb^max

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Maximum Bending Stress

Axial Thrust

Axial Thrust is the force exerted along the axis of a shaft in mechanical systems. It occurs when there is an imbalance of forces that acts in the direction parallel to the axis of rotation.

Symbol: P_axial

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Axial Thrust

Cross Sectional Area

Cross Sectional Area of Column is the area of a column that is obtained when a column is sliced perpendicular to some specified axis at a point.

Symbol: A_sectional

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Sectional Area

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Uniformly Distributed Load category

Go Bending Moment at Section for Strut subjected to Compressive Axial and Uniformly Distributed Load

M b = - (P axial \cdot δ) + (q f \cdot ((\frac{x^{2}}{2}) - (l column \cdot \frac{x}{2})))

Go Axial Thrust for Strut Subjected to Compressive Axial and Uniformly Distributed Load

P axial = \frac{- M b + (q f \cdot ((\frac{x^{2}}{2}) - (l column \cdot \frac{x}{2})))}{δ}

Go Deflection at Section for Strut Subjected to Compressive Axial and Uniformly Distributed Load

δ = \frac{- M b + (q f \cdot ((\frac{x^{2}}{2}) - (l column \cdot \frac{x}{2})))}{P axial}

Go Load Intensity for Strut Subjected to Compressive Axial and Uniformly Distributed Load

q f = \frac{M b + (P axial \cdot δ)}{(\frac{x^{2}}{2}) - (l column \cdot \frac{x}{2})}

How to Evaluate Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load?

Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load evaluator uses Moment of Inertia = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum Bending Stress-(Axial Thrust/Cross Sectional Area)))) to evaluate the Moment of Inertia, The Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load formula is defined as a measure of the strut's resistance to bending under the influence of a uniformly distributed load and an axial compressive force, providing a critical value for structural integrity. Moment of Inertia is denoted by I symbol.

How to evaluate Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load using this online evaluator? To use this online evaluator for Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load, enter Maximum Bending Moment In Column (M), Distance from Neutral Axis to Extreme Point (c), Maximum Bending Stress (σb^max), Axial Thrust (P_axial) & Cross Sectional Area (A_sectional) and hit the calculate button.

FAQs on Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load

What is the formula to find Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load?

The formula of Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load is expressed as Moment of Inertia = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum Bending Stress-(Axial Thrust/Cross Sectional Area)))). Here is an example- 8E+8 = (16*0.01/((2000000-(1500/1.4)))).

How to calculate Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load?

With Maximum Bending Moment In Column (M), Distance from Neutral Axis to Extreme Point (c), Maximum Bending Stress (σb^max), Axial Thrust (P_axial) & Cross Sectional Area (A_sectional) we can find Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load using the formula - Moment of Inertia = (Maximum Bending Moment In Column*Distance from Neutral Axis to Extreme Point/((Maximum Bending Stress-(Axial Thrust/Cross Sectional Area)))).

Can the Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load be negative?

No, the Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load, measured in Second Moment of Area cannot be negative.

Which unit is used to measure Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load?

Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load is usually measured using the Centimeter⁴[cm⁴] for Second Moment of Area. Meter⁴[cm⁴], Millimeter⁴[cm⁴] are the few other units in which Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load can be measured.

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Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load Formula

Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load Example

Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load Solution

Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load Formula Elements

Other formulas in Strut Subjected to Compressive Axial Thrust and a Transverse Uniformly Distributed Load category

How to Evaluate Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load?

FAQs on Moment of Inertia given Maximum Stress for Strut Subjected to Uniformly Distributed Load

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