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Radius of Gyration of Column given Elastic Critical Buckling Load Formula

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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. Check FAQs

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

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

Radius of Gyration of Column given Elastic Critical Buckling Load Example

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Here is how the Radius of Gyration of Column given Elastic Critical Buckling Load equation looks like with Values.

Here is how the Radius of Gyration of Column given Elastic Critical Buckling Load equation looks like with Units.

Here is how the Radius of Gyration of Column given Elastic Critical Buckling Load equation looks like.

11.4136 = \sqrt{\frac{5 \cdot 3000^{2}}{{3.1416}^{2} \cdot 50 \cdot 700}}

11.4136mm = \sqrt{\frac{5N \cdot {3000mm}^{2}}{{3.1416}^{2} \cdot 50MPa \cdot 700mm²}}

11.4136 = \sqrt{\frac{5 \cdot 3000^{2}}{{3.1416}^{2} \cdot 50 \cdot 700}}

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Radius of Gyration of Column given Elastic Critical Buckling Load Solution

Follow our step by step solution on how to calculate Radius of Gyration of Column given Elastic Critical Buckling Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r gyration = \sqrt{\frac{5N \cdot {3000mm}^{2}}{π^{2} \cdot 50MPa \cdot 700mm²}}

Next Step Substitute values of Constants

∴

r gyration = \sqrt{\frac{5N \cdot {3000mm}^{2}}{{3.1416}^{2} \cdot 50MPa \cdot 700mm²}}

Next Step Prepare to Evaluate

∴

r gyration = \sqrt{\frac{5 \cdot 3000^{2}}{{3.1416}^{2} \cdot 50 \cdot 700}}

Next Step Evaluate

∴

r gyration = 0.0114135924780252m

Next Step Convert to Output's Unit

∴

r gyration = 11.4135924780252mm

LAST Step Rounding Answer

∴

r gyration = 11.4136mm

Radius of Gyration of Column given Elastic Critical Buckling Load Formula Elements

Variables

Constants

Functions

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

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

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

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 Slenderness Ratio given Elastic Critical Buckling Load

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

How to Evaluate Radius of Gyration of Column given Elastic Critical Buckling Load?

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

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

FAQs on Radius of Gyration of Column given Elastic Critical Buckling Load

What is the formula to find Radius of Gyration of Column given Elastic Critical Buckling Load?

The formula of Radius of Gyration of Column given Elastic Critical Buckling Load is expressed as Radius of Gyration of Column = sqrt((Buckling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity*Column Cross-Sectional Area)). Here is an example- 11.41359 = sqrt((5*3^2)/(pi^2*50000000*0.0007)).

How to calculate Radius of Gyration of Column given Elastic Critical Buckling Load?

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

Can the Radius of Gyration of Column given Elastic Critical Buckling Load be negative?

No, the Radius of Gyration of Column given Elastic Critical Buckling Load, measured in Length cannot be negative.

Which unit is used to measure Radius of Gyration of Column given Elastic Critical Buckling Load?

Radius of Gyration of Column given Elastic Critical Buckling Load is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Radius of Gyration of Column given Elastic Critical Buckling Load can be measured.

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Radius of Gyration of Column given Elastic Critical Buckling Load Formula

Radius of Gyration of Column given Elastic Critical Buckling Load Example

Radius of Gyration of Column given Elastic Critical Buckling Load Solution

Radius of Gyration of Column given Elastic Critical Buckling Load Formula Elements

Other formulas in Slender Columns category

How to Evaluate Radius of Gyration of Column given Elastic Critical Buckling Load?

FAQs on Radius of Gyration of Column given Elastic Critical Buckling Load

Variable Name