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Allowable Compression Stress given Slenderness Ratio Formula

GoAllowable Compression Stress when Slenderness Ratio is less than Cc Formula

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The Allowable Compression Stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied to a structural material. Check FAQs

F a = \frac{12 \cdot (π^{2}) \cdot E s}{23 \cdot (λ^{2})}

F_a - Allowable Compression Stress?E_s - Modulus of Elasticity of Steel?λ - Slenderness Ratio?π - Archimedes' constant?

Allowable Compression Stress given Slenderness Ratio Example

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Here is how the Allowable Compression Stress given Slenderness Ratio equation looks like with Values.

Here is how the Allowable Compression Stress given Slenderness Ratio equation looks like with Units.

Here is how the Allowable Compression Stress given Slenderness Ratio equation looks like.

4.3255 = \frac{12 \cdot ({3.1416}^{2}) \cdot 210000}{23 \cdot ({0.5}^{2})}

4.3255MPa = \frac{12 \cdot ({3.1416}^{2}) \cdot 210000MPa}{23 \cdot ({0.5}^{2})}

4.3255 = \frac{12 \cdot ({3.1416}^{2}) \cdot 210000}{23 \cdot ({0.5}^{2})}

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Allowable Compression Stress given Slenderness Ratio Solution

Follow our step by step solution on how to calculate Allowable Compression Stress given Slenderness Ratio?

FIRST Step Consider the formula

F a = \frac{12 \cdot (π^{2}) \cdot E s}{23 \cdot (λ^{2})}

Next Step Substitute values of Variables

∴

F a = \frac{12 \cdot (π^{2}) \cdot 210000MPa}{23 \cdot ({0.5}^{2})}

Next Step Substitute values of Constants

∴

F a = \frac{12 \cdot ({3.1416}^{2}) \cdot 210000MPa}{23 \cdot ({0.5}^{2})}

Next Step Prepare to Evaluate

∴

F a = \frac{12 \cdot ({3.1416}^{2}) \cdot 210000}{23 \cdot ({0.5}^{2})}

Next Step Evaluate

∴

F a = 4325461.40708612Pa

Next Step Convert to Output's Unit

∴

F a = 4.32546140708612MPa

LAST Step Rounding Answer

∴

F a = 4.3255MPa

Allowable Compression Stress given Slenderness Ratio Formula Elements

Variables

Constants

Allowable Compression Stress

The Allowable Compression Stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied to a structural material.

Symbol: F_a

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Allowable Compression Stress

Modulus of Elasticity 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.

Symbol: E_s

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Steel

Slenderness Ratio

Slenderness Ratio is the ratio of the length of a column and the least radius of gyration of its cross section.

Symbol: λ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Slenderness Ratio

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Allowable Compression Stress

Go Allowable Compression Stress when Slenderness Ratio is less than Cc

F a = \frac{1 - (\frac{λ^{2}}{2 \cdot {C c}^{2}})}{(\frac{5}{3}) + (3 \cdot \frac{λ}{8 \cdot C c}) - (\frac{λ^{3}}{8 \cdot ({C c}^{3})})} \cdot F y

Other formulas in Axially Loaded Steel Columns Design category

Go Slenderness Ratio between Inelastic from Elastic Buckling

λ = \sqrt{\frac{2 \cdot (π^{2}) \cdot E s}{F y}}

How to Evaluate Allowable Compression Stress given Slenderness Ratio?

Allowable Compression Stress given Slenderness Ratio evaluator uses Allowable Compression Stress = (12*(pi^2)*Modulus of Elasticity of Steel)/(23*(Slenderness Ratio^2)) to evaluate 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 evaluate Allowable Compression Stress given Slenderness Ratio using this online evaluator? To use this online evaluator for Allowable Compression Stress given Slenderness Ratio, enter Modulus of Elasticity of Steel (E_s) & Slenderness Ratio (λ) and hit the calculate button.

FAQs on Allowable Compression Stress given Slenderness Ratio

What is the formula to find Allowable Compression Stress given Slenderness Ratio?

The formula of Allowable Compression Stress given Slenderness Ratio is expressed as Allowable Compression Stress = (12*(pi^2)*Modulus of Elasticity of Steel)/(23*(Slenderness Ratio^2)). Here is an example- 4.3E-6 = (12*(pi^2)*210000000000)/(23*(0.5^2)).

How to calculate Allowable Compression Stress given Slenderness Ratio?

With Modulus of Elasticity of Steel (E_s) & Slenderness Ratio (λ) we can find Allowable Compression Stress given Slenderness Ratio using the formula - Allowable Compression Stress = (12*(pi^2)*Modulus of Elasticity of Steel)/(23*(Slenderness Ratio^2)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Allowable Compression Stress?

Here are the different ways to Calculate Allowable Compression Stress-

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

Can the Allowable Compression Stress given Slenderness Ratio be negative?

No, the Allowable Compression Stress given Slenderness Ratio, measured in Pressure cannot be negative.

Which unit is used to measure Allowable Compression Stress given Slenderness Ratio?

Allowable Compression Stress given Slenderness Ratio is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Allowable Compression Stress given Slenderness Ratio can be measured.

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Allowable Compression Stress given Slenderness Ratio Formula

​GoAllowable Compression Stress when Slenderness Ratio is less than Cc Formula

Allowable Compression Stress given Slenderness Ratio Example

Allowable Compression Stress given Slenderness Ratio Solution

Allowable Compression Stress given Slenderness Ratio Formula Elements

Other Formulas to find Allowable Compression Stress

Other formulas in Axially Loaded Steel Columns Design category

How to Evaluate Allowable Compression Stress given Slenderness Ratio?

FAQs on Allowable Compression Stress given Slenderness Ratio

Variable Name

GoAllowable Compression Stress when Slenderness Ratio is less than Cc Formula