Transition from Long to Short Column Range 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%
✖Aluminum Constant is a material constant which is used in calculations for stress–strain behavior.ⓘ Aluminum Constant [k]			+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 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%

✖The Slenderness Ratio of Column is the ratio of the length of a column and the least radius of gyration of its cross section.ⓘ Transition from Long to Short Column Range [λ]

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Transition from Long to Short Column Range Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness Ratio of Column = pi*(sqrt(End Fixity Coefficient*Aluminum Constant*Modulus of Elasticity/Column Yield Stress))
λ = pi*(sqrt(c*k*E/F_ce))
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

Slenderness Ratio of Column - The Slenderness Ratio of Column is the ratio of the length of a column and the least radius of gyration of its cross section.
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.
Aluminum Constant - Aluminum Constant is a material constant which is used in calculations for stress–strain behavior.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = pi*(sqrt(c*k*E/F_ce)) --> pi*(sqrt(4*3*50/15))

Evaluating ... ...

λ = 19.8691765315922

STEP 3: Convert Result to Output's Unit

19.8691765315922 --> No Conversion Required

FINAL ANSWER

19.8691765315922 ≈ 19.86918 <-- Slenderness Ratio of Column

(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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< 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

Transition from Long to Short Column Range Formula

LaTeX Go

Slenderness Ratio of Column = pi*(sqrt(End Fixity Coefficient*Aluminum Constant*Modulus of Elasticity/Column Yield Stress))
λ = pi*(sqrt(c*k*E/F_ce))

What is the difference between short column and long column?

The column, whose lateral dimension is very small when compared to its length (or height), is called a long column.
The column, whose lateral dimension is very large when compared to its length (or height), is called a short column.

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 Transition from Long to Short Column Range?

Transition from Long to Short Column Range calculator uses Slenderness Ratio of Column = pi*(sqrt(End Fixity Coefficient*Aluminum Constant*Modulus of Elasticity/Column Yield Stress)) to calculate the Slenderness Ratio of Column, The Transition from Long to Short Column Range formula is defined as the relation gives the transition between long and short column, where Euler equation is used for long aluminum columns, and depending on the material, either Johnson’s parabolic or straight-line equation is used for short columns. Slenderness Ratio of Column is denoted by λ symbol.

How to calculate Transition from Long to Short Column Range using this online calculator? To use this online calculator for Transition from Long to Short Column Range, enter End Fixity Coefficient (c), Aluminum Constant (k), Modulus of Elasticity (E) & Column Yield Stress (F_ce) and hit the calculate button. Here is how the Transition from Long to Short Column Range calculation can be explained with given input values -> 19.86918 = pi*(sqrt(4*3*50000000/15000000)).

FAQ

What is Transition from Long to Short Column Range?

The Transition from Long to Short Column Range formula is defined as the relation gives the transition between long and short column, where Euler equation is used for long aluminum columns, and depending on the material, either Johnson’s parabolic or straight-line equation is used for short columns and is represented as λ = pi*(sqrt(c*k*E/F_ce)) or Slenderness Ratio of Column = pi*(sqrt(End Fixity Coefficient*Aluminum Constant*Modulus of Elasticity/Column Yield Stress)). 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, Aluminum Constant is a material constant which is used in calculations for stress–strain behavior, 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 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.

How to calculate Transition from Long to Short Column Range?

The Transition from Long to Short Column Range formula is defined as the relation gives the transition between long and short column, where Euler equation is used for long aluminum columns, and depending on the material, either Johnson’s parabolic or straight-line equation is used for short columns is calculated using Slenderness Ratio of Column = pi*(sqrt(End Fixity Coefficient*Aluminum Constant*Modulus of Elasticity/Column Yield Stress)). To calculate Transition from Long to Short Column Range, you need End Fixity Coefficient (c), Aluminum Constant (k), Modulus of Elasticity (E) & Column Yield Stress (F_ce). With our tool, you need to enter the respective value for End Fixity Coefficient, Aluminum Constant, Modulus of Elasticity & Column Yield Stress 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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