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Allowable Compression Stress when Slenderness Ratio is less than Cc Formula

GoAllowable Compression Stress given Slenderness Ratio 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{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

F_a - Allowable Compression Stress?λ - Slenderness Ratio?C_c - Value of Cc?F_y - Minimum Specified Yield Stress of Steel?

Allowable Compression Stress when Slenderness Ratio is less than Cc Example

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Here is how the Allowable Compression Stress when Slenderness Ratio is less than Cc equation looks like with Values.

Here is how the Allowable Compression Stress when Slenderness Ratio is less than Cc equation looks like with Units.

Here is how the Allowable Compression Stress when Slenderness Ratio is less than Cc equation looks like.

16.5517 = \frac{1 - (\frac{{0.5}^{2}}{2 \cdot {0.75}^{2}})}{(\frac{5}{3}) + (3 \cdot \frac{0.5}{8 \cdot 0.75}) - (\frac{{0.5}^{3}}{8 \cdot ({0.75}^{3})})} \cdot 40

16.5517MPa = \frac{1 - (\frac{{0.5}^{2}}{2 \cdot {0.75}^{2}})}{(\frac{5}{3}) + (3 \cdot \frac{0.5}{8 \cdot 0.75}) - (\frac{{0.5}^{3}}{8 \cdot ({0.75}^{3})})} \cdot 40MPa

16.5517 = \frac{1 - (\frac{{0.5}^{2}}{2 \cdot {0.75}^{2}})}{(\frac{5}{3}) + (3 \cdot \frac{0.5}{8 \cdot 0.75}) - (\frac{{0.5}^{3}}{8 \cdot ({0.75}^{3})})} \cdot 40

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Allowable Compression Stress when Slenderness Ratio is less than Cc Solution

Follow our step by step solution on how to calculate Allowable Compression Stress when Slenderness Ratio is less than Cc?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F a = \frac{1 - (\frac{{0.5}^{2}}{2 \cdot {0.75}^{2}})}{(\frac{5}{3}) + (3 \cdot \frac{0.5}{8 \cdot 0.75}) - (\frac{{0.5}^{3}}{8 \cdot ({0.75}^{3})})} \cdot 40MPa

Next Step Convert Units

∴

F a = \frac{1 - (\frac{{0.5}^{2}}{2 \cdot {0.75}^{2}})}{(\frac{5}{3}) + (3 \cdot \frac{0.5}{8 \cdot 0.75}) - (\frac{{0.5}^{3}}{8 \cdot ({0.75}^{3})})} \cdot 4E+7Pa

Next Step Prepare to Evaluate

∴

F a = \frac{1 - (\frac{{0.5}^{2}}{2 \cdot {0.75}^{2}})}{(\frac{5}{3}) + (3 \cdot \frac{0.5}{8 \cdot 0.75}) - (\frac{{0.5}^{3}}{8 \cdot ({0.75}^{3})})} \cdot 4E+7

Next Step Evaluate

∴

F a = 16551724.137931Pa

Next Step Convert to Output's Unit

∴

F a = 16.551724137931MPa

LAST Step Rounding Answer

∴

F a = 16.5517MPa

Allowable Compression Stress when Slenderness Ratio is less than Cc Formula Elements

Variables

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

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

Value of Cc

Value of Cc is the value of Cc used in calculating allowable compression stress.

Symbol: C_c

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Value of Cc

Minimum Specified Yield Stress of Steel

Minimum Specified Yield Stress of Steel is the maximum stress that can be applied before it begins to change shape permanently.

Symbol: F_y

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Minimum Specified Yield Stress of Steel

Other Formulas to find Allowable Compression Stress

Go Allowable Compression Stress given Slenderness Ratio

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

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 when Slenderness Ratio is less than Cc?

Allowable Compression Stress when Slenderness Ratio is less than Cc evaluator 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 evaluate 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 evaluate Allowable Compression Stress when Slenderness Ratio is less than Cc using this online evaluator? To use this online evaluator 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.

FAQs on Allowable Compression Stress when Slenderness Ratio is less than Cc

What is the formula to find Allowable Compression Stress when Slenderness Ratio is less than Cc?

The formula of Allowable Compression Stress when Slenderness Ratio is less than Cc is expressed as 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. Here is an example- 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.

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

With Slenderness Ratio (λ), Value of Cc (C_c) & Minimum Specified Yield Stress of Steel (F_y) we can find Allowable Compression Stress when Slenderness Ratio is less than Cc using the formula - 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.

What are the other ways to Calculate Allowable Compression Stress?

Here are the different ways to Calculate Allowable Compression Stress-

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

Can the Allowable Compression Stress when Slenderness Ratio is less than Cc be negative?

No, the Allowable Compression Stress when Slenderness Ratio is less than Cc, measured in Pressure cannot be negative.

Which unit is used to measure Allowable Compression Stress when Slenderness Ratio is less than Cc?

Allowable Compression Stress when Slenderness Ratio is less than Cc 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 when Slenderness Ratio is less than Cc can be measured.

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Allowable Compression Stress when Slenderness Ratio is less than Cc Formula

​GoAllowable Compression Stress given Slenderness Ratio Formula

Allowable Compression Stress when Slenderness Ratio is less than Cc Example

Allowable Compression Stress when Slenderness Ratio is less than Cc Solution

Allowable Compression Stress when Slenderness Ratio is less than Cc Formula Elements

Other Formulas to find Allowable Compression Stress

Other formulas in Axially Loaded Steel Columns Design category

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

FAQs on Allowable Compression Stress when Slenderness Ratio is less than Cc

Variable Name

GoAllowable Compression Stress given Slenderness Ratio Formula