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Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns Formula

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Radius of Gyration of Column is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass. Check FAQs

ρ = \sqrt{\frac{F e \cdot L^{2}}{c \cdot (π^{2}) \cdot E}}

ρ - Radius of Gyration of Column?F_e - Allowable Column Compressive Stress?L - Effective Length of Column?c - End Fixity Coefficient?E - Modulus of Elasticity?π - Archimedes' constant?

Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns Example

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Here is how the Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns equation looks like with Values.

Here is how the Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns equation looks like with Units.

Here is how the Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns equation looks like.

500.7693 = \sqrt{\frac{55 \cdot 3000^{2}}{4 \cdot ({3.1416}^{2}) \cdot 50}}

500.7693mm = \sqrt{\frac{55MPa \cdot {3000mm}^{2}}{4 \cdot ({3.1416}^{2}) \cdot 50MPa}}

500.7693 = \sqrt{\frac{55 \cdot 3000^{2}}{4 \cdot ({3.1416}^{2}) \cdot 50}}

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Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns Solution

Follow our step by step solution on how to calculate Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns?

FIRST Step Consider the formula

ρ = \sqrt{\frac{F e \cdot L^{2}}{c \cdot (π^{2}) \cdot E}}

Next Step Substitute values of Variables

∴

ρ = \sqrt{\frac{55MPa \cdot {3000mm}^{2}}{4 \cdot (π^{2}) \cdot 50MPa}}

Next Step Substitute values of Constants

∴

ρ = \sqrt{\frac{55MPa \cdot {3000mm}^{2}}{4 \cdot ({3.1416}^{2}) \cdot 50MPa}}

Next Step Convert Units

∴

ρ = \sqrt{\frac{55MPa \cdot {3m}^{2}}{4 \cdot ({3.1416}^{2}) \cdot 50MPa}}

Next Step Prepare to Evaluate

∴

ρ = \sqrt{\frac{55 \cdot 3^{2}}{4 \cdot ({3.1416}^{2}) \cdot 50}}

Next Step Evaluate

∴

ρ = 0.50076933763439m

Next Step Convert to Output's Unit

∴

ρ = 500.76933763439mm

LAST Step Rounding Answer

∴

ρ = 500.7693mm

Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns Formula Elements

Variables

Constants

Functions

Radius of Gyration of Column

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

Symbol: ρ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration of Column

Allowable Column Compressive Stress

Allowable Column Compressive Stress or allowable strength is defined as the maximum compressive stress that is allowed to be applied on a structural material like Column.

Symbol: F_e

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Allowable Column Compressive Stress

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

End Fixity Coefficient

The End Fixity Coefficient is defined as the ratio of the moment at one end to the moment at the same end when both the ends are ideally fixed.

Symbol: c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find End Fixity Coefficient

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

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 Allowable Design Loads for Aluminium Columns category

Go Length of Column given Allowable Compressive Stress for Aluminium Columns

L = \sqrt{\frac{c \cdot π^{2} \cdot E}{\frac{F e}{{(ρ)}^{2}}}}

Go Allowable Compressive Stress for Aluminium Columns

F e = \frac{c \cdot π^{2} \cdot E}{{(\frac{L}{ρ})}^{2}}

Go Allowable Compressive Stress for Aluminium Columns given Column Yield Stress

F e = F ce \cdot (1 - (K \cdot {(\frac{\frac{L}{ρ}}{π \cdot \sqrt{c \cdot \frac{E}{F ce}}})}^{k}))

Go Transition from Long to Short Column Range

λ = π \cdot (\sqrt{c \cdot k \cdot \frac{E}{F ce}})

How to Evaluate Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns?

Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns evaluator uses Radius of Gyration of Column = sqrt((Allowable Column Compressive Stress*Effective Length of Column^2)/(End Fixity Coefficient*(pi^2)*Modulus of Elasticity)) to evaluate the Radius of Gyration of Column, The Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns formula is defined as the length is used to describe the distribution of cross-sectional area in a column around its centroidal axis. Radius of Gyration of Column is denoted by ρ symbol.

How to evaluate Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns using this online evaluator? To use this online evaluator for Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns, enter Allowable Column Compressive Stress (F_e), Effective Length of Column (L), End Fixity Coefficient (c) & Modulus of Elasticity (E) and hit the calculate button.

FAQs on Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns

What is the formula to find Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns?

The formula of Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns is expressed as Radius of Gyration of Column = sqrt((Allowable Column Compressive Stress*Effective Length of Column^2)/(End Fixity Coefficient*(pi^2)*Modulus of Elasticity)). Here is an example- 500769.3 = sqrt((55000000*3^2)/(4*(pi^2)*50000000)).

How to calculate Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns?

With Allowable Column Compressive Stress (F_e), Effective Length of Column (L), End Fixity Coefficient (c) & Modulus of Elasticity (E) we can find Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns using the formula - Radius of Gyration of Column = sqrt((Allowable Column Compressive Stress*Effective Length of Column^2)/(End Fixity Coefficient*(pi^2)*Modulus of Elasticity)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns be negative?

No, the Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns, measured in Length cannot be negative.

Which unit is used to measure Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns?

Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns 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 Allowable Compressive Stress for Aluminium Columns can be measured.

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Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns Formula

Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns Example

Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns Solution

Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns Formula Elements

Other formulas in Allowable Design Loads for Aluminium Columns category

How to Evaluate Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns?

FAQs on Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns

Variable Name