Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Calculator

✖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.ⓘ Column Yield Stress [F_ce]			+10% -10%
✖Aluminum Alloy Constant K is a material's constant which is used in calculations for stress–strain behavior.ⓘ Aluminum Alloy Constant K [K]			+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%
✖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%
✖Aluminum Constant is a material constant which is used in calculations for stress–strain behavior.ⓘ Aluminum Constant [k]			+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 given Column Yield Stress [F_e]

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Allowable Compressive Stress for Aluminium Columns given Column Yield Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
F_e = F_ce*(1-(K*((L/ρ)/(pi*sqrt(c*E/F_ce)))^k))
This formula uses 1 Constants, 1 Functions, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

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.
Column Yield Stress - (Measured in Megapascal) - 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.
Aluminum Alloy Constant K - Aluminum Alloy Constant K is a material's constant which is used in calculations for stress–strain behavior.
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.
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.
Aluminum Constant - Aluminum Constant is a material constant which is used in calculations for stress–strain behavior.

STEP 1: Convert Input(s) to Base Unit

Column Yield Stress: 15 Megapascal --> 15 Megapascal No Conversion Required
Aluminum Alloy Constant K: 0.385 --> 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)
End Fixity Coefficient: 4 --> No Conversion Required
Modulus of Elasticity: 50 Megapascal --> 50 Megapascal No Conversion Required
Aluminum Constant: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_e = F_ce*(1-(K*((L/ρ)/(pi*sqrt(c*E/F_ce)))^k)) --> 15*(1-(0.385*((3/0.5)/(pi*sqrt(4*50/15)))^3))

Evaluating ... ...

F_e = 14.1736804712842

STEP 3: Convert Result to Output's Unit

14173680.4712842 Pascal -->14.1736804712842 Megapascal (Check conversion here)

FINAL ANSWER

14.1736804712842 ≈ 14.17368 Megapascal <-- Allowable Column Compressive Stress

(Calculation completed in 00.004 seconds)

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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 given Column Yield Stress Formula

LaTeX Go

What is Material Constants K, k & n for Aluminum Alloys?

Material constants K, k & n VALUES defined for Aluminum Alloys are as follows
for 14S_T4, 24S_T3, 24S_T4 & 61S_T6 are 0.385, 3 & 1 respectively,
for 14S_T6 & 75T are 0.25, 2 & 2 respectively.

Define 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 ends are ideally fixed.
c=2, both ends pivoted.
c=2.86, one pivoted, the 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 given Column Yield Stress?

Allowable Compressive Stress for Aluminium Columns given Column Yield Stress calculator 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 calculate 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 calculate Allowable Compressive Stress for Aluminium Columns given Column Yield Stress using this online calculator? To use this online calculator 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. Here is how the Allowable Compressive Stress for Aluminium Columns given Column Yield Stress calculation can be explained with given input values -> 1.4E-5 = 15000000*(1-(0.385*((3/0.5)/(pi*sqrt(4*50000000/15000000)))^3)).

FAQ

What is Allowable Compressive Stress for Aluminium Columns given Column Yield 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 and is represented as F_e = F_ce*(1-(K*((L/ρ)/(pi*sqrt(c*E/F_ce)))^k)) or 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)). 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, Aluminum Alloy Constant K is a material's constant which is used in calculations for stress–strain behavior, 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, 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 & Aluminum Constant is a material constant which is used in calculations for stress–strain behavior.

How to calculate Allowable Compressive Stress for Aluminium Columns given Column Yield 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 is calculated using 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 calculate Allowable Compressive Stress for Aluminium Columns given Column Yield Stress, you need 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). With our tool, you need to enter the respective value for Column Yield Stress, Aluminum Alloy Constant K, Effective Length of Column, Radius of Gyration of Column, End Fixity Coefficient, Modulus of Elasticity & Aluminum Constant 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 Column Yield Stress, Aluminum Alloy Constant K, Effective Length of Column, Radius of Gyration of Column, End Fixity Coefficient, Modulus of Elasticity & Aluminum Constant. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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