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Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Formula

GoAllowable Compressive Stress for Aluminium Columns 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 = F ce \cdot (1 - (K \cdot {(\frac{\frac{L}{ρ}}{π \cdot \sqrt{c \cdot \frac{E}{F ce}}})}^{k}))

F_e - Allowable Column Compressive Stress?F_ce - Column Yield Stress?K - Aluminum Alloy Constant K?L - Effective Length of Column?ρ - Radius of Gyration of Column?c - End Fixity Coefficient?E - Modulus of Elasticity?k - Aluminum Constant?π - Archimedes' constant?

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Example

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

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

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

14.1737 = 15 \cdot (1 - (0.385 \cdot {(\frac{\frac{3000}{500}}{3.1416 \cdot \sqrt{4 \cdot \frac{50}{15}}})}^{3}))

14.1737MPa = 15MPa \cdot (1 - (0.385 \cdot {(\frac{\frac{3000mm}{500mm}}{3.1416 \cdot \sqrt{4 \cdot \frac{50MPa}{15MPa}}})}^{3}))

14.1737 = 15 \cdot (1 - (0.385 \cdot {(\frac{\frac{3000}{500}}{3.1416 \cdot \sqrt{4 \cdot \frac{50}{15}}})}^{3}))

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Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F e = 15MPa \cdot (1 - (0.385 \cdot {(\frac{\frac{3000mm}{500mm}}{π \cdot \sqrt{4 \cdot \frac{50MPa}{15MPa}}})}^{3}))

Next Step Substitute values of Constants

∴

F e = 15MPa \cdot (1 - (0.385 \cdot {(\frac{\frac{3000mm}{500mm}}{3.1416 \cdot \sqrt{4 \cdot \frac{50MPa}{15MPa}}})}^{3}))

Next Step Convert Units

∴

F e = 15MPa \cdot (1 - (0.385 \cdot {(\frac{\frac{3m}{0.5m}}{3.1416 \cdot \sqrt{4 \cdot \frac{50MPa}{15MPa}}})}^{3}))

Next Step Prepare to Evaluate

∴

F e = 15 \cdot (1 - (0.385 \cdot {(\frac{\frac{3}{0.5}}{3.1416 \cdot \sqrt{4 \cdot \frac{50}{15}}})}^{3}))

Next Step Evaluate

∴

F e = 14173680.4712842Pa

Next Step Convert to Output's Unit

∴

F e = 14.1736804712842MPa

LAST Step Rounding Answer

∴

F e = 14.1737MPa

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Formula Elements

Variables

Constants

Functions

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.

Column Yield Stress

The column yield stress is the amount of stress that needs to be applied to a column to cause it to change from elastic deformation to plastic deformation.

Symbol: F_ce

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Aluminum Alloy Constant K

Aluminum Alloy Constant K is a material's constant which is used in calculations for stress–strain behavior.

Symbol: K

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

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.

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.

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.

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.

Aluminum Constant

Aluminum Constant is a material constant which is used in calculations for stress–strain behavior.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

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)

Credits

Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

Rudrani Tidke has created this Formula and 100+ more formulas!

Verified by Alithea Fernandes

Don Bosco College of Engineering (DBCE), Goa

Alithea Fernandes has verified this Formula and 100+ more formulas!

Other Formulas to find Allowable Column Compressive Stress

Go Allowable Compressive Stress for Aluminium Columns

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

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}}}}

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

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress evaluator uses 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)) to evaluate the Allowable Column Compressive Stress, Allowable Compressive Stress for Aluminium Columns given Column Yield Stress formula is defined as maximum stress (tensile, compressive or bending) that can be applied on 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 given Column Yield Stress using this online evaluator? To use this online evaluator for Allowable Compressive Stress for Aluminium Columns given Column Yield Stress, enter Column Yield Stress (F_ce), Aluminum Alloy Constant K (K), Effective Length of Column (L), Radius of Gyration of Column (ρ), End Fixity Coefficient (c), Modulus of Elasticity (E) & Aluminum Constant (k) and hit the calculate button.

FAQs on Allowable Compressive Stress for Aluminium Columns given Column Yield Stress

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

The formula of Allowable Compressive Stress for Aluminium Columns given Column Yield Stress is expressed as 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)). Here is an example- 1.4E-5 = 15000000*(1-(0.385*((3/0.5)/(pi*sqrt(4*50000000/15000000)))^3)).

How to calculate Allowable Compressive Stress for Aluminium Columns given Column Yield Stress?

With Column Yield Stress (F_ce), Aluminum Alloy Constant K (K), Effective Length of Column (L), Radius of Gyration of Column (ρ), End Fixity Coefficient (c), Modulus of Elasticity (E) & Aluminum Constant (k) we can find Allowable Compressive Stress for Aluminium Columns given Column Yield Stress using the formula - 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)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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=(End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Effective Length of Column/Radius of Gyration of Column)^2

Can the Allowable Compressive Stress for Aluminium Columns given Column Yield Stress be negative?

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

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

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress 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 given Column Yield Stress can be measured.

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Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Formula

​GoAllowable Compressive Stress for Aluminium Columns Formula

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Example

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Solution

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Formula Elements

Credits

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 given Column Yield Stress?

FAQs on Allowable Compressive Stress for Aluminium Columns given Column Yield Stress

Variable Name

GoAllowable Compressive Stress for Aluminium Columns Formula