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

✖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%
✖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%
✖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%

✖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 given Allowable Compressive Stress for Aluminium Columns [ρ]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Allowable Column Compressive Stress: 55 Megapascal --> 55 Megapascal No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3 Meter (Check conversion here)
End Fixity Coefficient: 4 --> No Conversion Required
Modulus of Elasticity: 50 Megapascal --> 50 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ = sqrt((F_e*L^2)/(c*(pi^2)*E)) --> sqrt((55*3^2)/(4*(pi^2)*50))

Evaluating ... ...

ρ = 0.50076933763439

STEP 3: Convert Result to Output's Unit

0.50076933763439 Meter -->500.76933763439 Millimeter (Check conversion here)

FINAL ANSWER

500.76933763439 ≈ 500.7693 Millimeter <-- Radius of Gyration 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

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

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))
ρ = sqrt((F_e*L^2)/(c*(pi^2)*E))

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

Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns calculator uses Radius of Gyration of Column = sqrt((Allowable Column Compressive Stress*Effective Length of Column^2)/(End Fixity Coefficient*(pi^2)*Modulus of Elasticity)) to calculate the Radius of Gyration of Column, The Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns formula is defined as the length is used to describe the distribution of cross-sectional area in a column around its centroidal axis. Radius of Gyration of Column is denoted by ρ symbol.

How to calculate Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns using this online calculator? To use this online calculator for Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns, enter Allowable Column Compressive Stress (F_e), Effective Length of Column (L), End Fixity Coefficient (c) & Modulus of Elasticity (E) and hit the calculate button. Here is how the Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns calculation can be explained with given input values -> 500769.3 = sqrt((55000000*3^2)/(4*(pi^2)*50000000)).

FAQ

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

The Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns formula is defined as the length is used to describe the distribution of cross-sectional area in a column around its centroidal axis and is represented as ρ = sqrt((F_e*L^2)/(c*(pi^2)*E)) or Radius of Gyration of Column = sqrt((Allowable Column Compressive Stress*Effective Length of Column^2)/(End Fixity Coefficient*(pi^2)*Modulus of Elasticity)). 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, 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, 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.

How to calculate Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns?

The Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns formula is defined as the length is used to describe the distribution of cross-sectional area in a column around its centroidal axis is calculated using Radius of Gyration of Column = sqrt((Allowable Column Compressive Stress*Effective Length of Column^2)/(End Fixity Coefficient*(pi^2)*Modulus of Elasticity)). To calculate Radius of Gyration of Column given Allowable Compressive Stress for Aluminium Columns, you need Allowable Column Compressive Stress (F_e), Effective Length of Column (L), End Fixity Coefficient (c) & Modulus of Elasticity (E). With our tool, you need to enter the respective value for Allowable Column Compressive Stress, Effective Length of Column, End Fixity Coefficient & Modulus of Elasticity 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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