Allowable Compression Stress given Slenderness Ratio 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%
✖Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.ⓘ Slenderness Ratio [λ]			+10% -10%

✖The Allowable Compression Stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied to a structural material.ⓘ Allowable Compression Stress given Slenderness Ratio [F_a]

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Allowable Compression Stress given Slenderness Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Allowable Compression Stress = (12*(pi^2)*Modulus of Elasticity of Steel)/(23*(Slenderness Ratio^2))
F_a = (12*(pi^2)*E_s)/(23*(λ^2))
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Allowable Compression Stress - (Measured in Pascal) - The Allowable Compression Stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied to a structural material.
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.
Slenderness Ratio - Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity of Steel: 210000 Megapascal --> 210000 Megapascal No Conversion Required
Slenderness Ratio: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_a = (12*(pi^2)*E_s)/(23*(λ^2)) --> (12*(pi^2)*210000)/(23*(0.5^2))

Evaluating ... ...

F_a = 4325461.40708612

STEP 3: Convert Result to Output's Unit

4325461.40708612 Pascal -->4.32546140708612 Megapascal (Check conversion here)

FINAL ANSWER

4.32546140708612 ≈ 4.325461 Megapascal <-- Allowable Compression Stress

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Columns » Columns of Special Materials » Axially Loaded Steel Columns Design » Allowable Compression Stress given Slenderness Ratio

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< Axially Loaded Steel Columns Design Calculators

Allowable Compression Stress when Slenderness Ratio is less than Cc

LaTeX 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

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

Allowable Compression Stress given Slenderness Ratio

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

Allowable Compression Stress given Slenderness Ratio Formula

LaTeX Go

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

What is Allowable Compression Stress?

The allowable stress or allowable strength is the maximum stress (tensile, compressive or bending) that is allowed to be applied on a structural material.

Define Slenderness Ratio and it's purpose.

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.
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 Allowable Compression Stress given Slenderness Ratio?

Allowable Compression Stress given Slenderness Ratio calculator uses Allowable Compression Stress = (12*(pi^2)*Modulus of Elasticity of Steel)/(23*(Slenderness Ratio^2)) to calculate the Allowable Compression Stress, The Allowable Compression Stress given Slenderness Ratio is Greater than Cc formula calculates the LOWER OF maximum compression stress when it is known that slenderness ratio is more than Cc. Allowable Compression Stress is denoted by F_a symbol.

How to calculate Allowable Compression Stress given Slenderness Ratio using this online calculator? To use this online calculator for Allowable Compression Stress given Slenderness Ratio, enter Modulus of Elasticity of Steel (E_s) & Slenderness Ratio (λ) and hit the calculate button. Here is how the Allowable Compression Stress given Slenderness Ratio calculation can be explained with given input values -> 4.3E-6 = (12*(pi^2)*210000000000)/(23*(0.5^2)).

FAQ

What is Allowable Compression Stress given Slenderness Ratio?

The Allowable Compression Stress given Slenderness Ratio is Greater than Cc formula calculates the LOWER OF maximum compression stress when it is known that slenderness ratio is more than Cc and is represented as F_a = (12*(pi^2)*E_s)/(23*(λ^2)) or Allowable Compression Stress = (12*(pi^2)*Modulus of Elasticity of Steel)/(23*(Slenderness Ratio^2)). 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 & Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.

How to calculate Allowable Compression Stress given Slenderness Ratio?

The Allowable Compression Stress given Slenderness Ratio is Greater than Cc formula calculates the LOWER OF maximum compression stress when it is known that slenderness ratio is more than Cc is calculated using Allowable Compression Stress = (12*(pi^2)*Modulus of Elasticity of Steel)/(23*(Slenderness Ratio^2)). To calculate Allowable Compression Stress given Slenderness Ratio, you need Modulus of Elasticity of Steel (E_s) & Slenderness Ratio (λ). With our tool, you need to enter the respective value for Modulus of Elasticity of Steel & Slenderness Ratio 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 Compression Stress?

In this formula, Allowable Compression Stress uses Modulus of Elasticity of Steel & Slenderness Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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