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

Credits

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Created by Rudrani Tidke
Cummins College of Engineering for Women (CCEW), Pune
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Verified by Alithea Fernandes
Don Bosco College of Engineering (DBCE), Goa
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Allowable Design Loads for Aluminium Columns Calculators

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ Go Effective Length of Column = sqrt((End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Allowable Column Compressive Stress/(Radius of Gyration of Column)^2))
Allowable Compressive Stress for Aluminium Columns
​ LaTeX ​ 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

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