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Slenderness Ratio given Elastic Critical Buckling Load Formula

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Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section. Check FAQs

λ = \sqrt{\frac{π^{2} \cdot E \cdot A}{P Buckling Load}}

λ - Slenderness Ratio?E - Modulus of Elasticity?A - Column Cross-Sectional Area?P_{Buckling Load} - Buckling Load?π - Archimedes' constant?

Slenderness Ratio given Elastic Critical Buckling Load Example

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Here is how the Slenderness Ratio given Elastic Critical Buckling Load equation looks like with Values.

Here is how the Slenderness Ratio given Elastic Critical Buckling Load equation looks like with Units.

Here is how the Slenderness Ratio given Elastic Critical Buckling Load equation looks like.

262.8445 = \sqrt{\frac{{3.1416}^{2} \cdot 50 \cdot 700}{5}}

262.8445 = \sqrt{\frac{{3.1416}^{2} \cdot 50MPa \cdot 700mm²}{5N}}

262.8445 = \sqrt{\frac{{3.1416}^{2} \cdot 50 \cdot 700}{5}}

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Slenderness Ratio given Elastic Critical Buckling Load Solution

Follow our step by step solution on how to calculate Slenderness Ratio given Elastic Critical Buckling Load?

FIRST Step Consider the formula

λ = \sqrt{\frac{π^{2} \cdot E \cdot A}{P Buckling Load}}

Next Step Substitute values of Variables

∴

λ = \sqrt{\frac{π^{2} \cdot 50MPa \cdot 700mm²}{5N}}

Next Step Substitute values of Constants

∴

λ = \sqrt{\frac{{3.1416}^{2} \cdot 50MPa \cdot 700mm²}{5N}}

Next Step Prepare to Evaluate

∴

λ = \sqrt{\frac{{3.1416}^{2} \cdot 50 \cdot 700}{5}}

Next Step Evaluate

∴

λ = 262.844499291169

LAST Step Rounding Answer

∴

λ = 262.8445

Slenderness Ratio given Elastic Critical Buckling Load Formula Elements

Variables

Constants

Functions

Slenderness Ratio

Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.

Symbol: λ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Slenderness Ratio

Modulus of Elasticity

The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.

Symbol: E

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Column Cross-Sectional Area

Column Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Column Cross-Sectional Area

Buckling Load

The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity.

Symbol: P_{Buckling Load}

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Buckling Load

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 Slender Columns category

Go Elastic Critical Buckling Load

P Buckling Load = \frac{π^{2} \cdot E \cdot A}{{(\frac{L}{r gyration})}^{2}}

Go Cross-Sectional Area given Elastic Critical Buckling Load

A = \frac{P Buckling Load \cdot {(\frac{L}{r gyration})}^{2}}{π^{2} \cdot E}

Go Radius of Gyration of Column given Elastic Critical Buckling Load

r gyration = \sqrt{\frac{P Buckling Load \cdot L^{2}}{π^{2} \cdot E \cdot A}}

How to Evaluate Slenderness Ratio given Elastic Critical Buckling Load?

Slenderness Ratio given Elastic Critical Buckling Load evaluator uses Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load) to evaluate the Slenderness Ratio, The Slenderness Ratio given Elastic Critical Buckling Load formula is defined as the ratio used to describe the distribution of cross-sectional area in a column around its centroidal axis. Slenderness Ratio is denoted by λ symbol.

How to evaluate Slenderness Ratio given Elastic Critical Buckling Load using this online evaluator? To use this online evaluator for Slenderness Ratio given Elastic Critical Buckling Load, enter Modulus of Elasticity (E), Column Cross-Sectional Area (A) & Buckling Load (P_{Buckling Load}) and hit the calculate button.

FAQs on Slenderness Ratio given Elastic Critical Buckling Load

What is the formula to find Slenderness Ratio given Elastic Critical Buckling Load?

The formula of Slenderness Ratio given Elastic Critical Buckling Load is expressed as Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load). Here is an example- 262844.5 = sqrt((pi^2*50000000*0.0007)/5).

How to calculate Slenderness Ratio given Elastic Critical Buckling Load?

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

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Slenderness Ratio given Elastic Critical Buckling Load Formula

Slenderness Ratio given Elastic Critical Buckling Load Example

Slenderness Ratio given Elastic Critical Buckling Load Solution

Slenderness Ratio given Elastic Critical Buckling Load Formula Elements

Other formulas in Slender Columns category

How to Evaluate Slenderness Ratio given Elastic Critical Buckling Load?

FAQs on Slenderness Ratio given Elastic Critical Buckling Load

Variable Name