Allowable Compressive Stress for Aluminium Columns Calculator

✖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.ⓘ End Fixity Coefficient [c]			+10% -10%
✖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.ⓘ Modulus of Elasticity [E]			+10% -10%
✖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.ⓘ Effective Length of Column [L]			+10% -10%
✖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.ⓘ Radius of Gyration of Column [ρ]			+10% -10%

✖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.ⓘ Allowable Compressive Stress for Aluminium Columns [F_e]

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Formula

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Allowable Compressive Stress for Aluminium Columns

Formula

`"F"_{"e"} = ("c"*pi^2*"E")/("L"/"ρ")^2`

Example

`"54.83114MPa"=("4"*pi^2*"50MPa")/("3000mm"/"500mm")^2`

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Allowable Compressive Stress for Aluminium Columns Solution

STEP 0: Pre-Calculation Summary

Formula Used

Allowable Column Compressive Stress = (End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Effective Length of Column/Radius of Gyration of Column)^2
F_e = (c*pi^2*E)/(L/ρ)^2
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Allowable Column Compressive Stress - (Measured in Megapascal) - 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.
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.
Modulus of Elasticity - (Measured in Megapascal) - 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.
Effective Length of Column - (Measured in Meter) - 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.
Radius of Gyration of Column - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

End Fixity Coefficient: 4 --> No Conversion Required
Modulus of Elasticity: 50 Megapascal --> 50 Megapascal No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3 Meter (Check conversion here)
Radius of Gyration of Column: 500 Millimeter --> 0.5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_e = (c*pi^2*E)/(L/ρ)^2 --> (4*pi^2*50)/(3/0.5)^2

Evaluating ... ...

F_e = 54.8311355616075

STEP 3: Convert Result to Output's Unit

54831135.5616075 Pascal -->54.8311355616075 Megapascal (Check conversion here)

FINAL ANSWER

54.8311355616075 ≈ 54.83114 Megapascal <-- Allowable Column Compressive Stress

(Calculation completed in 00.004 seconds)

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Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

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< 5 Allowable Design Loads for Aluminium Columns Calculators

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress

Go 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))

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

Go Radius of Gyration of Column = sqrt((Allowable Column Compressive Stress*Effective Length of Column^2)/(End Fixity Coefficient*(pi^2)*Modulus of Elasticity))

Length of Column given Allowable Compressive Stress for Aluminium Columns

Go Effective Length of Column = sqrt((End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Allowable Column Compressive Stress/(Radius of Gyration of Column)^2))

Transition from Long to Short Column Range

Go Slenderness Ratio of Column = pi*(sqrt(End Fixity Coefficient*Aluminum Constant*Modulus of Elasticity/Column Yield Stress))

Allowable Compressive Stress for Aluminium Columns

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

Allowable Compressive Stress for Aluminium Columns Formula

Allowable Column Compressive Stress = (End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Effective Length of Column/Radius of Gyration of Column)^2
F_e = (c*pi^2*E)/(L/ρ)^2

What is 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.
c=2, both ends pivoted;
c=2.86, one pivoted, other fixed;
c=1.25 to 1.50,Restraining bulkhead partially fixed;
c=4, both ends fixed;
c=1 one fixed, one free.

How to Calculate Allowable Compressive Stress for Aluminium Columns?

Allowable Compressive Stress for Aluminium Columns calculator uses Allowable Column Compressive Stress = (End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Effective Length of Column/Radius of Gyration of Column)^2 to calculate 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 calculate Allowable Compressive Stress for Aluminium Columns using this online calculator? To use this online calculator 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. Here is how the Allowable Compressive Stress for Aluminium Columns calculation can be explained with given input values -> 5.5E-5 = (4*pi^2*50000000)/(3/0.5)^2.

FAQ

What is Allowable Compressive Stress for Aluminium Columns?

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 and is represented as F_e = (c*pi^2*E)/(L/ρ)^2 or Allowable Column Compressive Stress = (End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Effective Length of Column/Radius of Gyration of Column)^2. 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, 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, 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 & 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.

How to calculate Allowable Compressive Stress for Aluminium Columns?

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 is calculated using Allowable Column Compressive Stress = (End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Effective Length of Column/Radius of Gyration of Column)^2. To calculate Allowable Compressive Stress for Aluminium Columns, you need End Fixity Coefficient (c), Modulus of Elasticity (E), Effective Length of Column (L) & Radius of Gyration of Column (ρ). With our tool, you need to enter the respective value for End Fixity Coefficient, Modulus of Elasticity, Effective Length of Column & Radius of Gyration of Column and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Allowable Column Compressive Stress?

In this formula, Allowable Column Compressive Stress uses End Fixity Coefficient, Modulus of Elasticity, Effective Length of Column & Radius of Gyration of Column. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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