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Critical Buckling Load Formula

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

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

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

Critical Buckling Load Example

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Here is how the Critical Buckling Load equation looks like with Values.

Here is how the Critical Buckling Load equation looks like with Units.

Here is how the Critical Buckling Load equation looks like.

5304.9124 = 0.0688 \cdot (\frac{{3.1416}^{2} \cdot 2E+11}{160^{2}})

5304.9124kN = 0.0688m² \cdot (\frac{{3.1416}^{2} \cdot 2E+11N/m²}{160^{2}})

5304.9124 = 0.0688 \cdot (\frac{{3.1416}^{2} \cdot 2E+11}{160^{2}})

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Critical Buckling Load Solution

Follow our step by step solution on how to calculate Critical Buckling Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

P cr = 0.0688m² \cdot (\frac{π^{2} \cdot 2E+11N/m²}{160^{2}})

Next Step Substitute values of Constants

∴

P cr = 0.0688m² \cdot (\frac{{3.1416}^{2} \cdot 2E+11N/m²}{160^{2}})

Next Step Convert Units

∴

P cr = 0.0688m² \cdot (\frac{{3.1416}^{2} \cdot 2E+11Pa}{160^{2}})

Next Step Prepare to Evaluate

∴

P cr = 0.0688 \cdot (\frac{{3.1416}^{2} \cdot 2E+11}{160^{2}})

Next Step Evaluate

∴

P cr = 5304912.36558553N

Next Step Convert to Output's Unit

∴

P cr = 5304.91236558553kN

LAST Step Rounding Answer

∴

P cr = 5304.9124kN

Critical Buckling Load Formula Elements

Variables

Constants

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

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

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

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

Other formulas in Drill String Buckling category

Go Cross Section Area of Column for Critical Buckling Load

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

Go Column Slenderness Ratio for Critical Buckling Load

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

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 Critical Buckling Load?

Critical Buckling Load evaluator uses Critical Buckling Load for Drill String = Cross Section Area of Column*((pi^2*Elastic Modulus)/(Column Slenderness Ratio^2)) to evaluate the Critical Buckling Load for Drill String, The Critical Buckling Load formula is defined as the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally. Critical Buckling Load for Drill String is denoted by P_cr symbol.

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

FAQs on Critical Buckling Load

What is the formula to find Critical Buckling Load?

The formula of Critical Buckling Load is expressed as Critical Buckling Load for Drill String = Cross Section Area of Column*((pi^2*Elastic Modulus)/(Column Slenderness Ratio^2)). Here is an example- 5.304912 = 0.0688*((pi^2*200000000000)/(160^2)).

How to calculate Critical Buckling Load?

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

Can the Critical Buckling Load be negative?

Yes, the Critical Buckling Load, measured in Force can be negative.

Which unit is used to measure Critical Buckling Load?

Critical Buckling Load is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Critical Buckling Load can be measured.

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Critical Buckling Load Formula

Critical Buckling Load Example

Critical Buckling Load Solution

Critical Buckling Load Formula Elements

Other formulas in Drill String Buckling category

How to Evaluate Critical Buckling Load?

FAQs on Critical Buckling Load

Variable Name