Allowable Compression Stress when Slenderness Ratio is less than Cc Calculator

✖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%
✖Value of Cc is the value of Cc used in calculating allowable compression stress.ⓘ Value of Cc [C_c]			+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%

✖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 when Slenderness Ratio is less than Cc [F_a]

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Allowable Compression Stress when Slenderness Ratio is less than Cc

Formula

`"F"_{"a"} = (1-(("λ"^2)/(2*"C"_{"c"}^2)))/((5/3)+(3*"λ"/(8*"C"_{"c"}))-(("λ"^3)/(8*("C"_{"c"}^3))))*"F"_{"y"}`

Example

`"16.55172MPa"=(1-((("0.5")^2)/(2*("0.75")^2)))/((5/3)+(3*"0.5"/(8*"0.75"))-((("0.5")^3)/(8*(("0.75")^3))))*"40MPa"`

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Allowable Compression Stress when Slenderness Ratio is less than Cc Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
F_a = (1-((λ^2)/(2*C_c^2)))/((5/3)+(3*λ/(8*C_c))-((λ^3)/(8*(C_c^3))))*F_y
This formula uses 4 Variables

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.
Slenderness Ratio - Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.
Value of Cc - Value of Cc is the value of Cc used in calculating allowable compression stress.
Minimum Specified Yield Stress of Steel - (Measured in Pascal) - 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

Slenderness Ratio: 0.5 --> No Conversion Required
Value of Cc: 0.75 --> No Conversion Required
Minimum Specified Yield Stress of Steel: 40 Megapascal --> 40000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_a = (1-((λ^2)/(2*C_c^2)))/((5/3)+(3*λ/(8*C_c))-((λ^3)/(8*(C_c^3))))*F_y --> (1-((0.5^2)/(2*0.75^2)))/((5/3)+(3*0.5/(8*0.75))-((0.5^3)/(8*(0.75^3))))*40000000

Evaluating ... ...

F_a = 16551724.137931

STEP 3: Convert Result to Output's Unit

16551724.137931 Pascal -->16.551724137931 Megapascal (Check conversion here)

FINAL ANSWER

16.551724137931 ≈ 16.55172 Megapascal <-- Allowable Compression Stress

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Columns » Columns of Special Materials » Axially Loaded Steel Columns Design » Allowable Compression Stress when Slenderness Ratio is less than Cc

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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 when Slenderness Ratio is less than Cc Formula

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 when Slenderness Ratio is less than Cc?

Allowable Compression Stress when Slenderness Ratio is less than Cc calculator uses 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 to calculate the Allowable Compression Stress, The Allowable Compression Stress when Slenderness Ratio is less than Cc formula calculates the LOWER OF maximum compression stress when it is known that slenderness ratio is less than Cc. Allowable Compression Stress is denoted by F_a symbol.

How to calculate Allowable Compression Stress when Slenderness Ratio is less than Cc using this online calculator? To use this online calculator for Allowable Compression Stress when Slenderness Ratio is less than Cc, enter Slenderness Ratio (λ), Value of Cc (C_c) & Minimum Specified Yield Stress of Steel (F_y) and hit the calculate button. Here is how the Allowable Compression Stress when Slenderness Ratio is less than Cc calculation can be explained with given input values -> 1.7E-5 = (1-((0.5^2)/(2*0.75^2)))/((5/3)+(3*0.5/(8*0.75))-((0.5^3)/(8*(0.75^3))))*40000000.

FAQ

What is Allowable Compression Stress when Slenderness Ratio is less than Cc?

The Allowable Compression Stress when Slenderness Ratio is less than Cc formula calculates the LOWER OF maximum compression stress when it is known that slenderness ratio is less than Cc and is represented as F_a = (1-((λ^2)/(2*C_c^2)))/((5/3)+(3*λ/(8*C_c))-((λ^3)/(8*(C_c^3))))*F_y or 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 is the ratio of the length of a column and the least radius of gyration of its cross section, Value of Cc is the value of Cc used in calculating allowable compression stress & Minimum Specified Yield Stress of Steel is the maximum stress that can be applied before it begins to change shape permanently.

How to calculate Allowable Compression Stress when Slenderness Ratio is less than Cc?

The Allowable Compression Stress when Slenderness Ratio is less than Cc formula calculates the LOWER OF maximum compression stress when it is known that slenderness ratio is less than Cc is calculated using 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. To calculate Allowable Compression Stress when Slenderness Ratio is less than Cc, you need Slenderness Ratio (λ), Value of Cc (C_c) & Minimum Specified Yield Stress of Steel (F_y). With our tool, you need to enter the respective value for Slenderness Ratio, Value of Cc & 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.

How many ways are there to calculate Allowable Compression Stress?

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

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

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