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Allowable Compressive Stress for Aluminium Columns Formula

GoAllowable Compressive Stress for Aluminium Columns given Column Yield Stress Formula

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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. Check FAQs

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

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

Allowable Compressive Stress for Aluminium Columns Example

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

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

Here is how the Allowable Compressive Stress for Aluminium Columns equation looks like.

54.8311 = \frac{4 \cdot {3.1416}^{2} \cdot 50}{{(\frac{3000}{500})}^{2}}

54.8311MPa = \frac{4 \cdot {3.1416}^{2} \cdot 50MPa}{{(\frac{3000mm}{500mm})}^{2}}

54.8311 = \frac{4 \cdot {3.1416}^{2} \cdot 50}{{(\frac{3000}{500})}^{2}}

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Allowable Compressive Stress for Aluminium Columns Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F e = \frac{4 \cdot π^{2} \cdot 50MPa}{{(\frac{3000mm}{500mm})}^{2}}

Next Step Substitute values of Constants

∴

F e = \frac{4 \cdot {3.1416}^{2} \cdot 50MPa}{{(\frac{3000mm}{500mm})}^{2}}

Next Step Convert Units

∴

F e = \frac{4 \cdot {3.1416}^{2} \cdot 50MPa}{{(\frac{3m}{0.5m})}^{2}}

Next Step Prepare to Evaluate

∴

F e = \frac{4 \cdot {3.1416}^{2} \cdot 50}{{(\frac{3}{0.5})}^{2}}

Next Step Evaluate

∴

F e = 54831135.5616075Pa

Next Step Convert to Output's Unit

∴

F e = 54.8311355616075MPa

LAST Step Rounding Answer

∴

F e = 54.8311MPa

Allowable Compressive Stress for Aluminium Columns Formula Elements

Variables

Constants

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

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

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

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

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 to find Allowable Column Compressive Stress

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}))

Other formulas in Allowable Design Loads for Aluminium Columns category

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

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

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 Transition from Long to Short Column Range

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

How to Evaluate Allowable Compressive Stress for Aluminium Columns?

Allowable Compressive Stress for Aluminium Columns evaluator uses Allowable Column Compressive Stress = (End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Effective Length of Column/Radius of Gyration of Column)^2 to evaluate the Allowable Column Compressive Stress, The Allowable Compressive Stress for Aluminium Columns formula is defined as the maximum stress (tensile, compressive or bending) that can be applied on a structural material such as Aluminium Columns without any deformation. Allowable Column Compressive Stress is denoted by F_e symbol.

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

FAQs on Allowable Compressive Stress for Aluminium Columns

What is the formula to find Allowable Compressive Stress for Aluminium Columns?

The formula of Allowable Compressive Stress for Aluminium Columns is expressed as Allowable Column Compressive Stress = (End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Effective Length of Column/Radius of Gyration of Column)^2. Here is an example- 5.5E-5 = (4*pi^2*50000000)/(3/0.5)^2.

How to calculate Allowable Compressive Stress for Aluminium Columns?

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

What are the other ways to Calculate Allowable Column Compressive Stress?

Here are the different ways to Calculate Allowable Column Compressive Stress-

Allowable Column Compressive Stress=Column Yield Stress*(1-(Aluminum Alloy Constant K*((Effective Length of Column/Radius of Gyration of Column)/(pi*sqrt(End Fixity Coefficient*Modulus of Elasticity/Column Yield Stress)))^Aluminum Constant))

Can the Allowable Compressive Stress for Aluminium Columns be negative?

No, the Allowable Compressive Stress for Aluminium Columns, measured in Stress cannot be negative.

Which unit is used to measure Allowable Compressive Stress for Aluminium Columns?

Allowable Compressive Stress for Aluminium Columns is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Allowable Compressive Stress for Aluminium Columns can be measured.

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Allowable Compressive Stress for Aluminium Columns Formula

​GoAllowable Compressive Stress for Aluminium Columns given Column Yield Stress Formula

Allowable Compressive Stress for Aluminium Columns Example

Allowable Compressive Stress for Aluminium Columns Solution

Allowable Compressive Stress for Aluminium Columns Formula Elements

Other Formulas to find Allowable Column Compressive Stress

Other formulas in Allowable Design Loads for Aluminium Columns category

How to Evaluate Allowable Compressive Stress for Aluminium Columns?

FAQs on Allowable Compressive Stress for Aluminium Columns

Variable Name

GoAllowable Compressive Stress for Aluminium Columns given Column Yield Stress Formula