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Length of Column given Allowable Compressive Stress for Aluminium Columns Formula

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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. Check FAQs
L=c⋅π2⋅EFe(ρ)2
L - Effective Length of Column?c - End Fixity Coefficient?E - Modulus of Elasticity?Fe - Allowable Column Compressive Stress?ρ - Radius of Gyration of Column?π - Archimedes' constant?

Length of Column given Allowable Compressive Stress for Aluminium Columns Example

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

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

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

2995.3911Edit=4Edit⋅3.14162⋅50Edit55Edit(500Edit)2
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Length of Column given Allowable Compressive Stress for Aluminium Columns Solution

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

FIRST Step Consider the formula
L=c⋅π2⋅EFe(ρ)2
Next Step Substitute values of Variables
∴ L=4⋅π2⋅50MPa55MPa(500mm)2
Next Step Substitute values of Constants
∴ L=4⋅3.14162⋅50MPa55MPa(500mm)2
Next Step Convert Units
∴ L=4⋅3.14162⋅50MPa55MPa(0.5m)2
Next Step Prepare to Evaluate
∴ L=4⋅3.14162⋅5055(0.5)2
Next Step Evaluate
∴L=2.99539106584666m
Next Step Convert to Output's Unit
∴L=2995.39106584666mm
LAST Step Rounding Answer
∴L=2995.3911mm

Length of Column given Allowable Compressive Stress for Aluminium Columns Formula Elements

Variables
Constants
Functions
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 ColumnOpen Variable
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 CoefficientOpen Variable
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 ElasticityOpen Variable
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: Fe
Measurement: StressUnit: MPa
Note: Value should be greater than 0.
Formulas to find Allowable Column Compressive StressOpen Variable
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 ColumnOpen Variable
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 Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns
ρ=Fe⋅L2c⋅(π2)⋅E
​Go Allowable Compressive Stress for Aluminium Columns
Fe=c⋅π2⋅E(Lρ)2
​Go Allowable Compressive Stress for Aluminium Columns given Column Yield Stress
Fe=Fce⋅(1-(K⋅(Lρπ⋅c⋅EFce)k))
​Go Transition from Long to Short Column Range
λ=π⋅(c⋅k⋅EFce)

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

Length of Column given Allowable Compressive Stress for Aluminium Columns evaluator uses Effective Length of Column = sqrt((End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Allowable Column Compressive Stress/(Radius of Gyration of Column)^2)) to evaluate the Effective Length of Column, The Length of Column given Allowable Compressive Stress for Aluminium Columns formula is defined as distance between two points where column gets its fixidty of support so its movement is restrained in all directions. Effective Length of Column is denoted by L symbol.

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

FAQs on Length of Column given Allowable Compressive Stress for Aluminium Columns

What is the formula to find Length of Column given Allowable Compressive Stress for Aluminium Columns?
The formula of Length of Column given Allowable Compressive Stress for Aluminium Columns is expressed as Effective Length of Column = sqrt((End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Allowable Column Compressive Stress/(Radius of Gyration of Column)^2)). Here is an example- 3E+6 = sqrt((4*pi^2*50000000)/(55000000/(0.5)^2)).
How to calculate Length of Column given Allowable Compressive Stress for Aluminium Columns?
With End Fixity Coefficient (c), Modulus of Elasticity (E), Allowable Column Compressive Stress (Fe) & Radius of Gyration of Column (ρ) we can find Length of Column given Allowable Compressive Stress for Aluminium Columns using the formula - Effective Length of Column = sqrt((End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Allowable Column Compressive Stress/(Radius of Gyration of Column)^2)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).
Can the Length of Column given Allowable Compressive Stress for Aluminium Columns be negative?
No, the Length of Column given Allowable Compressive Stress for Aluminium Columns, measured in Length cannot be negative.
Which unit is used to measure Length of Column given Allowable Compressive Stress for Aluminium Columns?
Length 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 Length of Column given Allowable Compressive Stress for Aluminium Columns can be measured.
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