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Column Slenderness Ratio for Critical Buckling Load Formula

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Column Slenderness Ratio is defined as the ratio of length l to the radius of gyration. Check FAQs

Lcr ratio = \sqrt{\frac{A \cdot π^{2} \cdot E}{P cr}}

Lcr_ratio - Column Slenderness Ratio?A - Cross Section Area of Column?E - Elastic Modulus?P_cr - Critical Buckling Load for Drill String?π - Archimedes' constant?

Column Slenderness Ratio for Critical Buckling Load Example

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Here is how the Column Slenderness Ratio for Critical Buckling Load equation looks like with Values.

Here is how the Column Slenderness Ratio for Critical Buckling Load equation looks like with Units.

Here is how the Column Slenderness Ratio for Critical Buckling Load equation looks like.

160 = \sqrt{\frac{0.0688 \cdot {3.1416}^{2} \cdot 2E+11}{5304.912}}

160 = \sqrt{\frac{0.0688m² \cdot {3.1416}^{2} \cdot 2E+11N/m²}{5304.912kN}}

160 = \sqrt{\frac{0.0688 \cdot {3.1416}^{2} \cdot 2E+11}{5304.912}}

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Column Slenderness Ratio for Critical Buckling Load Solution

Follow our step by step solution on how to calculate Column Slenderness Ratio for Critical Buckling Load?

FIRST Step Consider the formula

Lcr ratio = \sqrt{\frac{A \cdot π^{2} \cdot E}{P cr}}

Next Step Substitute values of Variables

∴

Lcr ratio = \sqrt{\frac{0.0688m² \cdot π^{2} \cdot 2E+11N/m²}{5304.912kN}}

Next Step Substitute values of Constants

∴

Lcr ratio = \sqrt{\frac{0.0688m² \cdot {3.1416}^{2} \cdot 2E+11N/m²}{5304.912kN}}

Next Step Convert Units

∴

Lcr ratio = \sqrt{\frac{0.0688m² \cdot {3.1416}^{2} \cdot 2E+11Pa}{5.3E+6N}}

Next Step Prepare to Evaluate

∴

Lcr ratio = \sqrt{\frac{0.0688 \cdot {3.1416}^{2} \cdot 2E+11}{5.3E+6}}

Next Step Evaluate

∴

Lcr ratio = 160.000005513163

LAST Step Rounding Answer

∴

Lcr ratio = 160

Column Slenderness Ratio for Critical Buckling Load Formula Elements

Variables

Constants

Functions

Column Slenderness Ratio

Column Slenderness Ratio is defined as the ratio of length l to the radius of gyration.

Symbol: Lcr_ratio

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Column Slenderness Ratio

Cross Section Area of Column

Cross Section Area of Column is the shape we get when cutting straight through the column.

Symbol: A

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Cross Section Area of Column

Elastic Modulus

Elastic Modulus is the fundamental property of materials that measures their stiffness or resistance to elastic deformation under stress.

Symbol: E

Measurement: StressUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Elastic Modulus

Critical Buckling Load for Drill String

Critical Buckling Load for Drill String is defined as the greatest load that will not cause lateral deflection.

Symbol: P_cr

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Critical Buckling Load for Drill String

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 in Drill String Buckling category

Go Critical Buckling Load

P cr = A \cdot (\frac{π^{2} \cdot E}{{Lcr ratio}^{2}})

Go Cross Section Area of Column for Critical Buckling Load

A = \frac{P cr \cdot {Lcr ratio}^{2}}{π^{2} \cdot E}

Go Reynolds Number in Shorter Length of Pipe

Re = \frac{V flow \cdot D p}{v}

Go Flow Velocity given Reynolds Number in Shorter Length of Pipe

V flow = \frac{Re \cdot v}{D p}

How to Evaluate Column Slenderness Ratio for Critical Buckling Load?

Column Slenderness Ratio for Critical Buckling Load evaluator uses Column Slenderness Ratio = sqrt((Cross Section Area of Column*pi^2*Elastic Modulus)/Critical Buckling Load for Drill String) to evaluate the Column Slenderness Ratio, The Column Slenderness Ratio for Critical Buckling Load is defined as the ratio of length l to the radius of gyration. Column Slenderness Ratio is denoted by Lcr_ratio symbol.

How to evaluate Column Slenderness Ratio for Critical Buckling Load using this online evaluator? To use this online evaluator for Column Slenderness Ratio for Critical Buckling Load, enter Cross Section Area of Column (A), Elastic Modulus (E) & Critical Buckling Load for Drill String (P_cr) and hit the calculate button.

FAQs on Column Slenderness Ratio for Critical Buckling Load

What is the formula to find Column Slenderness Ratio for Critical Buckling Load?

The formula of Column Slenderness Ratio for Critical Buckling Load is expressed as Column Slenderness Ratio = sqrt((Cross Section Area of Column*pi^2*Elastic Modulus)/Critical Buckling Load for Drill String). Here is an example- 160 = sqrt((0.0688*pi^2*200000000000)/5304912).

How to calculate Column Slenderness Ratio for Critical Buckling Load?

With Cross Section Area of Column (A), Elastic Modulus (E) & Critical Buckling Load for Drill String (P_cr) we can find Column Slenderness Ratio for Critical Buckling Load using the formula - Column Slenderness Ratio = sqrt((Cross Section Area of Column*pi^2*Elastic Modulus)/Critical Buckling Load for Drill String). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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Column Slenderness Ratio for Critical Buckling Load Formula

Column Slenderness Ratio for Critical Buckling Load Example

Column Slenderness Ratio for Critical Buckling Load Solution

Column Slenderness Ratio for Critical Buckling Load Formula Elements

Other formulas in Drill String Buckling category

How to Evaluate Column Slenderness Ratio for Critical Buckling Load?

FAQs on Column Slenderness Ratio for Critical Buckling Load

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