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Allowable Compressive Stress when Slenderness Ratio is Less than Cc Formula

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GoAllowable Compressive Stress when Slenderness Ratio is Greater 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{(1 - (\frac{{(\frac{k \cdot l}{r})}^{2}}{2 \cdot {C c}^{2}})) \cdot F y}{F s}

F_a - Allowable Compression Stress?k - Effective Length Factor?l - Effective Column Length?r - Radius of Gyration?C_c - Factor for Allowable Stress Design?F_y - Yield Stress of Steel?F_s - Safety Factor?

Allowable Compressive Stress when Slenderness Ratio is Less than Cc Example

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

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

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

140.6352 = \frac{(1 - (\frac{{(\frac{0.75 \cdot 3000}{87})}^{2}}{2 \cdot {125.66}^{2}})) \cdot 250}{1.74}

140.6352MPa = \frac{(1 - (\frac{{(\frac{0.75 \cdot 3000mm}{87mm})}^{2}}{2 \cdot {125.66}^{2}})) \cdot 250MPa}{1.74}

140.6352 = \frac{(1 - (\frac{{(\frac{0.75 \cdot 3000}{87})}^{2}}{2 \cdot {125.66}^{2}})) \cdot 250}{1.74}

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Home » Engineering » Civil » Design of Steel Structures » Allowable Compressive Stress when Slenderness Ratio is Less than Cc

Allowable Compressive Stress when Slenderness Ratio is Less than Cc Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F a = \frac{(1 - (\frac{{(\frac{0.75 \cdot 3000mm}{87mm})}^{2}}{2 \cdot {125.66}^{2}})) \cdot 250MPa}{1.74}

Next Step Convert Units

∴

F a = \frac{(1 - (\frac{{(\frac{0.75 \cdot 3m}{0.087m})}^{2}}{2 \cdot {125.66}^{2}})) \cdot 2.5E+8Pa}{1.74}

Next Step Prepare to Evaluate

∴

F a = \frac{(1 - (\frac{{(\frac{0.75 \cdot 3}{0.087})}^{2}}{2 \cdot {125.66}^{2}})) \cdot 2.5E+8}{1.74}

Next Step Evaluate

∴

F a = 140635222.350094Pa

Next Step Convert to Output's Unit

∴

F a = 140.635222350094MPa

LAST Step Rounding Answer

∴

F a = 140.6352MPa

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

Variables

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.

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.

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.

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.

Factor for Allowable Stress Design

Factor for Allowable Stress Design is the usual term used to demarcate between inelastic and elastic member buckling.

Symbol: C_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Yield Stress of Steel

Yield Stress of Steel is the stress at which the material begins to deform plastically, meaning it will not return to its original shape when the applied force is removed.

Symbol: F_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Safety Factor

Safety factor otherwise called as factor of safety expresses how much stronger a system is than it needs to be for an intended load.

Symbol: F_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Credits

Creator Image

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Formula and 500+ more formulas!

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Formula and 2600+ more formulas!

Other Formulas to find Allowable Compression Stress

Go Allowable Compressive Stress when Slenderness Ratio is Greater than Cc

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

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}}

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

Allowable Compressive Stress when Slenderness Ratio is Less than Cc evaluator uses 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 to evaluate the Allowable Compression Stress, The Allowable Compressive Stress when Slenderness Ratio is Less 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 less than the slenderness ratio. Allowable Compression Stress is denoted by F_a symbol.

How to evaluate Allowable Compressive Stress when Slenderness Ratio is Less than Cc using this online evaluator? To use this online evaluator for Allowable Compressive Stress when Slenderness Ratio is Less than Cc, enter Effective Length Factor (k), Effective Column Length (l), Radius of Gyration (r), Factor for Allowable Stress Design (C_c), Yield Stress of Steel (F_y) & Safety Factor (F_s) and hit the calculate button.

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

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

The formula of Allowable Compressive Stress when Slenderness Ratio is Less than Cc is expressed as 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. Here is an example- 0.000141 = ((1-((((0.75*3)/0.087)^2)/(2*125.66^2)))*250000000)/1.74.

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

With Effective Length Factor (k), Effective Column Length (l), Radius of Gyration (r), Factor for Allowable Stress Design (C_c), Yield Stress of Steel (F_y) & Safety Factor (F_s) we can find Allowable Compressive Stress when Slenderness Ratio is Less than Cc using the formula - 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.

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*((Effective Length Factor*Effective Column Length)/Radius of Gyration)^2)

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

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

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

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

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