Length of Column given 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%
✖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 Column Compressive Stress [F_e]			+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 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.ⓘ Length of Column given Allowable Compressive Stress for Aluminium Columns [L]

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Length of Column given Allowable Compressive Stress for Aluminium Columns Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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.
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
Allowable Column Compressive Stress: 55 Megapascal --> 55 Megapascal No Conversion Required
Radius of Gyration of Column: 500 Millimeter --> 0.5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = sqrt((c*pi^2*E)/(F_e/(ρ)^2)) --> sqrt((4*pi^2*50)/(55/(0.5)^2))

Evaluating ... ...

L = 2.99539106584666

STEP 3: Convert Result to Output's Unit

2.99539106584666 Meter -->2995.39106584666 Millimeter (Check conversion here)

FINAL ANSWER

2995.39106584666 ≈ 2995.391 Millimeter <-- Effective Length of Column

(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

Length of Column given Allowable Compressive Stress for Aluminium Columns Formula

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))
L = sqrt((c*pi^2*E)/(F_e/(ρ)^2))

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.

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.

How to Calculate Length of Column given Allowable Compressive Stress for Aluminium Columns?

Length of Column given Allowable Compressive Stress for Aluminium Columns calculator uses Effective Length of Column = sqrt((End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Allowable Column Compressive Stress/(Radius of Gyration of Column)^2)) to calculate the Effective Length of Column, The Length of Column given Allowable Compressive Stress for Aluminium Columns formula is defined as distance between two points where column gets its fixidty of support so its movement is restrained in all directions. Effective Length of Column is denoted by L symbol.

How to calculate Length of Column given Allowable Compressive Stress for Aluminium Columns using this online calculator? To use this online calculator for Length of Column given Allowable Compressive Stress for Aluminium Columns, enter End Fixity Coefficient (c), Modulus of Elasticity (E), Allowable Column Compressive Stress (F_e) & Radius of Gyration of Column (ρ) and hit the calculate button. Here is how the Length of Column given Allowable Compressive Stress for Aluminium Columns calculation can be explained with given input values -> 3E+6 = sqrt((4*pi^2*50000000)/(55000000/(0.5)^2)).

FAQ

What is Length of Column given Allowable Compressive Stress for Aluminium Columns?

The Length of Column given Allowable Compressive Stress for Aluminium Columns formula is defined as distance between two points where column gets its fixidty of support so its movement is restrained in all directions and is represented as L = sqrt((c*pi^2*E)/(F_e/(ρ)^2)) or Effective Length of Column = sqrt((End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Allowable Column Compressive Stress/(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, 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 & 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 Length of Column given Allowable Compressive Stress for Aluminium Columns?

The Length of Column given Allowable Compressive Stress for Aluminium Columns formula is defined as distance between two points where column gets its fixidty of support so its movement is restrained in all directions is calculated using Effective Length of Column = sqrt((End Fixity Coefficient*pi^2*Modulus of Elasticity)/(Allowable Column Compressive Stress/(Radius of Gyration of Column)^2)). To calculate Length of Column given Allowable Compressive Stress for Aluminium Columns, you need End Fixity Coefficient (c), Modulus of Elasticity (E), Allowable Column Compressive Stress (F_e) & Radius of Gyration of Column (ρ). With our tool, you need to enter the respective value for End Fixity Coefficient, Modulus of Elasticity, Allowable Column Compressive Stress & 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.

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