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Cross-Sectional Area given Elastic Critical Buckling Load Formula

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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. Check FAQs

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

A - Column Cross-Sectional Area?P_{Buckling Load} - Buckling Load?L - Effective Length of Column?r_gyration - Radius of Gyration of Column?E - Modulus of Elasticity?π - Archimedes' constant?

Cross-Sectional Area given Elastic Critical Buckling Load Example

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Here is how the Cross-Sectional Area given Elastic Critical Buckling Load equation looks like with Values.

Here is how the Cross-Sectional Area given Elastic Critical Buckling Load equation looks like with Units.

Here is how the Cross-Sectional Area given Elastic Critical Buckling Load equation looks like.

134.8951 = \frac{5 \cdot {(\frac{3000}{26})}^{2}}{{3.1416}^{2} \cdot 50}

134.8951mm² = \frac{5N \cdot {(\frac{3000mm}{26mm})}^{2}}{{3.1416}^{2} \cdot 50MPa}

134.8951 = \frac{5 \cdot {(\frac{3000}{26})}^{2}}{{3.1416}^{2} \cdot 50}

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Cross-Sectional Area given Elastic Critical Buckling Load Solution

Follow our step by step solution on how to calculate Cross-Sectional Area given Elastic Critical Buckling Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A = \frac{5N \cdot {(\frac{3000mm}{26mm})}^{2}}{π^{2} \cdot 50MPa}

Next Step Substitute values of Constants

∴

A = \frac{5N \cdot {(\frac{3000mm}{26mm})}^{2}}{{3.1416}^{2} \cdot 50MPa}

Next Step Prepare to Evaluate

∴

A = \frac{5 \cdot {(\frac{3000}{26})}^{2}}{{3.1416}^{2} \cdot 50}

Next Step Evaluate

∴

A = 0.000134895066979444m²

Next Step Convert to Output's Unit

∴

A = 134.895066979444mm²

LAST Step Rounding Answer

∴

A = 134.8951mm²

Cross-Sectional Area given Elastic Critical Buckling Load Formula Elements

Variables

Constants

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

Effective Length of Column

The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Radius of Gyration of Column

The Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.

Symbol: r_gyration

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration of Column

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

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 Slender Columns category

Go Elastic Critical Buckling Load

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

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}}

Go Slenderness Ratio given Elastic Critical Buckling Load

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

How to Evaluate Cross-Sectional Area given Elastic Critical Buckling Load?

Cross-Sectional Area given Elastic Critical Buckling Load evaluator uses Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity) to evaluate the Column Cross-Sectional Area, The Cross-Sectional Area given Elastic Critical Buckling Load is defined as the area of a two-dimensional shape obtained when a Column is sliced perpendicular to its length axis at a point. Column Cross-Sectional Area is denoted by A symbol.

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

FAQs on Cross-Sectional Area given Elastic Critical Buckling Load

What is the formula to find Cross-Sectional Area given Elastic Critical Buckling Load?

The formula of Cross-Sectional Area given Elastic Critical Buckling Load is expressed as Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity). Here is an example- 134.8951 = (5*(3/0.026)^2)/(pi^2*50000000).

How to calculate Cross-Sectional Area given Elastic Critical Buckling Load?

With Buckling Load (P_{Buckling Load}), Effective Length of Column (L), Radius of Gyration of Column (r_gyration) & Modulus of Elasticity (E) we can find Cross-Sectional Area given Elastic Critical Buckling Load using the formula - Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity). This formula also uses Archimedes' constant .

Can the Cross-Sectional Area given Elastic Critical Buckling Load be negative?

No, the Cross-Sectional Area given Elastic Critical Buckling Load, measured in Area cannot be negative.

Which unit is used to measure Cross-Sectional Area given Elastic Critical Buckling Load?

Cross-Sectional Area given Elastic Critical Buckling Load is usually measured using the Square Millimeter[mm²] for Area. Square Meter[mm²], Square Kilometer[mm²], Square Centimeter[mm²] are the few other units in which Cross-Sectional Area given Elastic Critical Buckling Load can be measured.

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Cross-Sectional Area given Elastic Critical Buckling Load Formula

Cross-Sectional Area given Elastic Critical Buckling Load Example

Cross-Sectional Area given Elastic Critical Buckling Load Solution

Cross-Sectional Area given Elastic Critical Buckling Load Formula Elements

Other formulas in Slender Columns category

How to Evaluate Cross-Sectional Area given Elastic Critical Buckling Load?

FAQs on Cross-Sectional Area given Elastic Critical Buckling Load

Variable Name