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

GoLength of Column given Max Bending Moment for Strut Subjected to 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 = ((\frac{x^{2}}{2}) - (\frac{M b + (P axial \cdot δ)}{q f})) \cdot \frac{2}{x}

l_column - Column Length?x - Distance of Deflection from End A?M_b - Bending Moment in Column?P_axial - Axial Thrust?δ - Deflection at Section of Column?q_f - Load Intensity?

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

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Here is how the Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load equation looks like with Values.

Here is how the Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load equation looks like with Units.

Here is how the Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load equation looks like.

-719.2857 = ((\frac{35^{2}}{2}) - (\frac{48 + (1500 \cdot 12)}{0.005})) \cdot \frac{2}{35}

-719.2857mm = ((\frac{{35mm}^{2}}{2}) - (\frac{48N*m + (1500N \cdot 12mm)}{0.005MPa})) \cdot \frac{2}{35mm}

-719.2857 = ((\frac{35^{2}}{2}) - (\frac{48 + (1500 \cdot 12)}{0.005})) \cdot \frac{2}{35}

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

Follow our step by step solution on how to calculate Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

l column = ((\frac{{35mm}^{2}}{2}) - (\frac{48N*m + (1500N \cdot 12mm)}{0.005MPa})) \cdot \frac{2}{35mm}

Next Step Convert Units

∴

l column = ((\frac{{0.035m}^{2}}{2}) - (\frac{48N*m + (1500N \cdot 0.012m)}{5000Pa})) \cdot \frac{2}{0.035m}

Next Step Prepare to Evaluate

∴

l column = ((\frac{{0.035}^{2}}{2}) - (\frac{48 + (1500 \cdot 0.012)}{5000})) \cdot \frac{2}{0.035}

Next Step Evaluate

∴

l column = -0.719285714285714m

Next Step Convert to Output's Unit

∴

l column = -719.285714285714mm

LAST Step Rounding Answer

∴

l column = -719.2857mm

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

Variables

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

Distance of Deflection from End A

Distance of Deflection from End A is the distance at which the deflection occurs in a beam or column, measured from one end of the beam, designated as End A.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance of Deflection from End A

Bending Moment in Column

Bending Moment in Column is the reaction induced in a column when an external force or moment is applied to the column, causing it to bend.

Symbol: M_b

Measurement: Moment of ForceUnit: N*m

Note: Value should be greater than 0.

Formulas to find Bending Moment in Column

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

Deflection at Section of Column

Deflection at Section of Column is the lateral displacement at the section of the column.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Deflection at Section of 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

Other Formulas to find Column Length

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

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

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 for Strut subjected to Compressive Axial and Uniformly Distributed Load?

Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load evaluator uses 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 to evaluate the Column Length, The Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load formula is defined as the maximum length of a strut that can withstand the compressive axial thrust and a transverse uniformly distributed load without buckling or failing, providing a safe and stable structural design. Column Length is denoted by l_column symbol.

How to evaluate Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load using this online evaluator? To use this online evaluator for Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load, enter Distance of Deflection from End A (x), Bending Moment in Column (M_b), Axial Thrust (P_axial), Deflection at Section of Column (δ) & Load Intensity (q_f) and hit the calculate button.

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

What is the formula to find Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load?

The formula of Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load is expressed as 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. Here is an example- -719285.714286 = (((0.035^2)/2)-((48+(1500*0.012))/5000))*2/0.035.

How to calculate Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load?

With Distance of Deflection from End A (x), Bending Moment in Column (M_b), Axial Thrust (P_axial), Deflection at Section of Column (δ) & Load Intensity (q_f) we can find Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load using the formula - 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.

What are the other ways to Calculate Column Length?

Here are the different ways to Calculate Column Length-

Column Length=sqrt(((Axial Thrust*Maximum Initial Deflection)-Maximum Bending Moment In Column)*8/(Load Intensity))

Can the Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load be negative?

No, the Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load, measured in Length cannot be negative.

Which unit is used to measure Length of Column for Strut subjected to Compressive Axial and Uniformly Distributed Load?

Length of Column for Strut subjected to Compressive Axial and 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 for Strut subjected to Compressive Axial and Uniformly Distributed Load can be measured.

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

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

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

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

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

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

Variable Name

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