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Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Formula

GoAllowable Compressive Stress when Slenderness Ratio is Less than Cc Formula

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

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

F_a - Allowable Compression Stress?E_s - Modulus of Elasticity of Steel?k - Effective Length Factor?l - Effective Column Length?r - Radius of Gyration?π - Archimedes' constant?

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Example

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

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

Here is how the Allowable Compressive Stress when Slenderness Ratio is Greater than Cc equation looks like.

1539.7727 = \frac{12 \cdot {3.1416}^{2} \cdot 200000}{23 \cdot {(\frac{0.75 \cdot 3000}{87})}^{2}}

1539.7727MPa = \frac{12 \cdot {3.1416}^{2} \cdot 200000MPa}{23 \cdot {(\frac{0.75 \cdot 3000mm}{87mm})}^{2}}

1539.7727 = \frac{12 \cdot {3.1416}^{2} \cdot 200000}{23 \cdot {(\frac{0.75 \cdot 3000}{87})}^{2}}

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Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F a = \frac{12 \cdot π^{2} \cdot 200000MPa}{23 \cdot {(\frac{0.75 \cdot 3000mm}{87mm})}^{2}}

Next Step Substitute values of Constants

∴

F a = \frac{12 \cdot {3.1416}^{2} \cdot 200000MPa}{23 \cdot {(\frac{0.75 \cdot 3000mm}{87mm})}^{2}}

Next Step Convert Units

∴

F a = \frac{12 \cdot {3.1416}^{2} \cdot 2E+11Pa}{23 \cdot {(\frac{0.75 \cdot 3m}{0.087m})}^{2}}

Next Step Prepare to Evaluate

∴

F a = \frac{12 \cdot {3.1416}^{2} \cdot 2E+11}{23 \cdot {(\frac{0.75 \cdot 3}{0.087})}^{2}}

Next Step Evaluate

∴

F a = 1539772716.76589Pa

Next Step Convert to Output's Unit

∴

F a = 1539.77271676589MPa

LAST Step Rounding Answer

∴

F a = 1539.7727MPa

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Formula Elements

Variables

Constants

Allowable Compression Stress

Allowable Compression Stress is the maximum stress (tensile, compressive or bending) that is allowed to be applied on 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 or elastic modulus is the resistance of the structure or object from being deformed elastically when a stress is applied.

Symbol: E_s

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Steel

Effective Length Factor

Effective Length Factor is the factor used for the members in the frame. It depends on the ratio of compression member stiffness to the end restraint stiffness.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Effective Length Factor

Effective Column Length

Effective Column Length of a column is the length of an equivalent pin-ended column that has the same load-carrying capacity and buckling behaviour as the actual column with different end conditions.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

Radius of Gyration

Radius of Gyration is the distance from the axis of rotation to a point where the total mass of any body is supposed to be concentrated.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration

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 Compressive Stress when Slenderness Ratio is Less than Cc

F a = \frac{(1 - (\frac{{(\frac{k \cdot l}{r})}^{2}}{2 \cdot {C c}^{2}})) \cdot F y}{F s}

Other formulas in Allowable Stress Design for Building Columns category

Go Slenderness Ratio Used for Separation

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

Go Factor for Unbraced Segment of any Cross-Section

C c = \frac{1986.66}{\sqrt{F y}}

Go Effective Length Factor

k = \frac{l}{l'}

Go Safety Factor for Allowable Compressive Stress

F s = \frac{5}{3} + (\frac{3 \cdot (\frac{k \cdot l}{r})}{8 \cdot C c}) - (\frac{{(\frac{k \cdot l}{r})}^{3}}{8 \cdot {C c}^{3}})

How to Evaluate Allowable Compressive Stress when Slenderness Ratio is Greater than Cc?

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc evaluator uses Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2) to evaluate the Allowable Compression Stress, The Allowable Compressive Stress when Slenderness Ratio is Greater than Cc formula is defined as the maximum limit of compressive stress that can be taken by the section when the condition specified is satisfied when the unbraced segment factor is greater than the slenderness ratio. Allowable Compression Stress is denoted by F_a symbol.

How to evaluate Allowable Compressive Stress when Slenderness Ratio is Greater than Cc using this online evaluator? To use this online evaluator for Allowable Compressive Stress when Slenderness Ratio is Greater than Cc, enter Modulus of Elasticity of Steel (E_s), Effective Length Factor (k), Effective Column Length (l) & Radius of Gyration (r) and hit the calculate button.

FAQs on Allowable Compressive Stress when Slenderness Ratio is Greater than Cc

What is the formula to find Allowable Compressive Stress when Slenderness Ratio is Greater than Cc?

The formula of Allowable Compressive Stress when Slenderness Ratio is Greater than Cc is expressed as Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2). Here is an example- 0.00154 = (12*pi^2*200000000000)/(23*((0.75*3)/0.087)^2).

How to calculate Allowable Compressive Stress when Slenderness Ratio is Greater than Cc?

With Modulus of Elasticity of Steel (E_s), Effective Length Factor (k), Effective Column Length (l) & Radius of Gyration (r) we can find Allowable Compressive Stress when Slenderness Ratio is Greater than Cc using the formula - Allowable Compression Stress = (12*pi^2*Modulus of Elasticity of Steel)/(23*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^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-((((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2)/(2*Factor for Allowable Stress Design^2)))*Yield Stress of Steel)/Safety Factor

Can the Allowable Compressive Stress when Slenderness Ratio is Greater than Cc be negative?

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

Which unit is used to measure Allowable Compressive Stress when Slenderness Ratio is Greater than Cc?

Allowable Compressive Stress when Slenderness Ratio is Greater 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 Compressive Stress when Slenderness Ratio is Greater than Cc can be measured.

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Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Formula

​GoAllowable Compressive Stress when Slenderness Ratio is Less than Cc Formula

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Example

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Solution

Allowable Compressive Stress when Slenderness Ratio is Greater than Cc Formula Elements

Other Formulas to find Allowable Compression Stress

Other formulas in Allowable Stress Design for Building Columns category

How to Evaluate Allowable Compressive Stress when Slenderness Ratio is Greater than Cc?

FAQs on Allowable Compressive Stress when Slenderness Ratio is Greater than Cc

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GoAllowable Compressive Stress when Slenderness Ratio is Less than Cc Formula