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Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula Example

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Here is how the Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula equation looks like with Values.

Here is how the Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula equation looks like with Units.

Here is how the Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula Solution

Follow our step by step solution on how to calculate Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

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 Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Pin Ended Columns category

Go Critical Buckling Load for Pin Ended Columns by Euler's Formula

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

Go Cross-Sectional Area given Critical Buckling Load for Pin Ended Columns by Euler's Formula

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

Go Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula

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

How to Evaluate Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Critical Buckling Load for Pin Ended Columns by Euler's formula is defined as a function of elastic modulus, critical buckling load, and cross-sectional area of the column. Slenderness Ratio is denoted by λ symbol.

How to evaluate Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula using this online evaluator? To use this online evaluator for Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula, 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula

What is the formula to find Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

The formula of Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula?

With Modulus of Elasticity (E), Column Cross-Sectional Area (A) & Buckling Load (P_{Buckling Load}) we can find Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 Critical Buckling Load for Pin Ended Columns by Euler's Formula Formula

Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula Example

Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula Solution

Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula Formula Elements

Other formulas in Pin Ended Columns category

How to Evaluate Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

FAQs on Slenderness Ratio given Critical Buckling Load for Pin Ended Columns by Euler's Formula

Variable Name