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Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load Formula

GoLength of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load Formula

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Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions. Check FAQs

l column = \sqrt{((P axial \cdot C) - M) \cdot \frac{8}{q f}}

l_column - Column Length?P_axial - Axial Thrust?C - Maximum Initial Deflection?M - Maximum Bending Moment In Column?q_f - Load Intensity?

Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load Example

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Here is how the Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load equation looks like with Values.

Here is how the Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load equation looks like with Units.

Here is how the Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load equation looks like.

215.4066 = \sqrt{((1500 \cdot 30) - 16) \cdot \frac{8}{0.005}}

215.4066mm = \sqrt{((1500N \cdot 30mm) - 16N*m) \cdot \frac{8}{0.005MPa}}

215.4066 = \sqrt{((1500 \cdot 30) - 16) \cdot \frac{8}{0.005}}

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Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load?

FIRST Step Consider the formula

l column = \sqrt{((P axial \cdot C) - M) \cdot \frac{8}{q f}}

Next Step Substitute values of Variables

∴

l column = \sqrt{((1500N \cdot 30mm) - 16N*m) \cdot \frac{8}{0.005MPa}}

Next Step Convert Units

∴

l column = \sqrt{((1500N \cdot 0.03m) - 16N*m) \cdot \frac{8}{5000Pa}}

Next Step Prepare to Evaluate

∴

l column = \sqrt{((1500 \cdot 0.03) - 16) \cdot \frac{8}{5000}}

Next Step Evaluate

∴

l column = 0.21540659228538m

Next Step Convert to Output's Unit

∴

l column = 215.40659228538mm

LAST Step Rounding Answer

∴

l column = 215.4066mm

Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load Formula Elements

Variables

Functions

Column Length

Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l_column

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

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

Maximum Initial Deflection

Maximum Initial Deflection is the greatest amount of displacement or bending that occurs in a mechanical structure or component when a load is first applied.

Symbol: C

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Maximum Initial Deflection

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

Load Intensity

Load Intensity is the distribution of load over a certain area or length of a structural element.

Symbol: q_f

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Load Intensity

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Column Length

Go Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load

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

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 Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load?

Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load evaluator uses Column Length = sqrt(((Axial Thrust*Maximum Initial Deflection)-Maximum Bending Moment In Column)*8/(Load Intensity)) to evaluate the Column Length, The Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load formula is defined as the maximum length of a column that can withstand a given axial compressive thrust and a transverse uniformly distributed load without buckling or failing. Column Length is denoted by l_column symbol.

How to evaluate Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load using this online evaluator? To use this online evaluator for Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load, enter Axial Thrust (P_axial), Maximum Initial Deflection (C), Maximum Bending Moment In Column (M) & Load Intensity (q_f) and hit the calculate button.

FAQs on Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load

What is the formula to find Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load?

The formula of Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load is expressed as Column Length = sqrt(((Axial Thrust*Maximum Initial Deflection)-Maximum Bending Moment In Column)*8/(Load Intensity)). Here is an example- 215406.6 = sqrt(((1500*0.03)-16)*8/(5000)).

How to calculate Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load?

With Axial Thrust (P_axial), Maximum Initial Deflection (C), Maximum Bending Moment In Column (M) & Load Intensity (q_f) we can find Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load using the formula - Column Length = sqrt(((Axial Thrust*Maximum Initial Deflection)-Maximum Bending Moment In Column)*8/(Load Intensity)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Column Length?

Here are the different ways to Calculate Column Length-

Column Length=(((Distance of Deflection from End A^2)/2)-((Bending Moment in Column+(Axial Thrust*Deflection at Section of Column))/Load Intensity))*2/Distance of Deflection from End A

Can the Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load be negative?

No, the Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load, measured in Length cannot be negative.

Which unit is used to measure Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load?

Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load can be measured.

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Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load Formula

​GoLength of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load Formula

Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load Example

Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load Solution

Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load Formula Elements

Other Formulas to find Column Length

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

How to Evaluate Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load?

FAQs on Length of Column given Max Bending Moment for Strut Subjected to Uniformly Distributed Load

Variable Name

GoLength of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load Formula