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))
Fa = (12*(pi^2)*Es)/(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
Fa = (12*(pi^2)*Es)/(23*(λ^2)) --> (12*(pi^2)*210000)/(23*(0.5^2))
Evaluating ... ...
Fa = 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 00.004 seconds)

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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))

Allowable Compression Stress given Slenderness Ratio Formula

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