Slenderness Ratio between Inelastic from Elastic Buckling Calculator

✖The Modulus of Elasticity of Steel is a characteristic that assesses steel's resistance to deformation under load. It is the ratio of stress to strain.ⓘ Modulus of Elasticity of Steel [E_s]			+10% -10%
✖Minimum Specified Yield Stress of Steel is the maximum stress that can be applied before it begins to change shape permanently.ⓘ Minimum Specified Yield Stress of Steel [F_y]			+10% -10%

✖Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.ⓘ Slenderness Ratio between Inelastic from Elastic Buckling [λ]

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Formula

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Slenderness Ratio between Inelastic from Elastic Buckling

Formula

`"λ" = sqrt((2*(pi^2)*"E"_{"s"})/"F"_{"y"})`

Example

`"321.9175"=sqrt((2*(pi^2)*"210000MPa")/"40MPa")`

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Slenderness Ratio between Inelastic from Elastic Buckling Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slenderness Ratio = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Minimum Specified Yield Stress of Steel)
λ = sqrt((2*(pi^2)*E_s)/F_y)
This formula uses 1 Constants, 1 Functions, 3 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 - Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
Modulus of Elasticity of Steel - (Measured in Megapascal) - The Modulus of Elasticity of Steel is a characteristic that assesses steel's resistance to deformation under load. It is the ratio of stress to strain.
Minimum Specified Yield Stress of Steel - (Measured in Megapascal) - Minimum Specified Yield Stress of Steel is the maximum stress that can be applied before it begins to change shape permanently.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity of Steel: 210000 Megapascal --> 210000 Megapascal No Conversion Required
Minimum Specified Yield Stress of Steel: 40 Megapascal --> 40 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = sqrt((2*(pi^2)*E_s)/F_y) --> sqrt((2*(pi^2)*210000)/40)

Evaluating ... ...

λ = 321.91745248035

STEP 3: Convert Result to Output's Unit

321.91745248035 --> No Conversion Required

FINAL ANSWER

321.91745248035 ≈ 321.9175 <-- Slenderness Ratio

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Columns » Columns of Special Materials » Axially Loaded Steel Columns Design » Slenderness Ratio between Inelastic from Elastic Buckling

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Created by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

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Cummins College of Engineering for Women (CCEW), Pune

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< 3 Axially Loaded Steel Columns Design Calculators

Allowable Compression Stress when Slenderness Ratio is less than Cc

Go Allowable Compression Stress = (1-((Slenderness Ratio^2)/(2*Value of Cc^2)))/((5/3)+(3*Slenderness Ratio/(8*Value of Cc))-((Slenderness Ratio^3)/(8*(Value of Cc^3))))*Minimum Specified Yield Stress of Steel

Slenderness Ratio between Inelastic from Elastic Buckling

Go Slenderness Ratio = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Minimum Specified Yield Stress of Steel)

Allowable Compression Stress given Slenderness Ratio

Go Allowable Compression Stress = (12*(pi^2)*Modulus of Elasticity of Steel)/(23*(Slenderness Ratio^2))

Slenderness Ratio between Inelastic from Elastic Buckling Formula

Slenderness Ratio = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Minimum Specified Yield Stress of Steel)
λ = sqrt((2*(pi^2)*E_s)/F_y)

What is Slenderness Ratio?

It is defined as the effective length of the column and the least radius of gyration, the latter defined by the area of the cross-section of the column and is the second moment of the area of the cross-section.

What is the purpose of Slenderness Ratio?

It is used extensively for finding out the design load as well as in classifying various columns in short/intermediate/long. The slenderness ratio of a column gives an indication of buckling failure in the column. The more the slenderness ratio, more the tendency of a column to fail by buckling effect in that direction.

How to Calculate Slenderness Ratio between Inelastic from Elastic Buckling?

Slenderness Ratio between Inelastic from Elastic Buckling calculator uses Slenderness Ratio = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Minimum Specified Yield Stress of Steel) to calculate the Slenderness Ratio, The Slenderness Ratio between Inelastic from Elastic Buckling formula calculates the measure of slenderness which is a measure of the propensity of a column to buckle. Slenderness Ratio is denoted by λ symbol.

How to calculate Slenderness Ratio between Inelastic from Elastic Buckling using this online calculator? To use this online calculator for Slenderness Ratio between Inelastic from Elastic Buckling, enter Modulus of Elasticity of Steel (E_s) & Minimum Specified Yield Stress of Steel (F_y) and hit the calculate button. Here is how the Slenderness Ratio between Inelastic from Elastic Buckling calculation can be explained with given input values -> 321.9175 = sqrt((2*(pi^2)*210000000000)/40000000).

FAQ

What is Slenderness Ratio between Inelastic from Elastic Buckling?

The Slenderness Ratio between Inelastic from Elastic Buckling formula calculates the measure of slenderness which is a measure of the propensity of a column to buckle and is represented as λ = sqrt((2*(pi^2)*E_s)/F_y) or Slenderness Ratio = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Minimum Specified Yield Stress of Steel). The Modulus of Elasticity of Steel is a characteristic that assesses steel's resistance to deformation under load. It is the ratio of stress to strain & Minimum Specified Yield Stress of Steel is the maximum stress that can be applied before it begins to change shape permanently.

How to calculate Slenderness Ratio between Inelastic from Elastic Buckling?

The Slenderness Ratio between Inelastic from Elastic Buckling formula calculates the measure of slenderness which is a measure of the propensity of a column to buckle is calculated using Slenderness Ratio = sqrt((2*(pi^2)*Modulus of Elasticity of Steel)/Minimum Specified Yield Stress of Steel). To calculate Slenderness Ratio between Inelastic from Elastic Buckling, you need Modulus of Elasticity of Steel (E_s) & Minimum Specified Yield Stress of Steel (F_y). With our tool, you need to enter the respective value for Modulus of Elasticity of Steel & Minimum Specified Yield Stress of Steel 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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