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Allowable Stress when Slenderness Ratio is Less than Cc Formula

GoAllowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications Formula

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The allowable stresses in columns is the material failure stress (a property of the material) divided by a factor of safety greater than one. Check FAQs

F a = (\frac{f y}{2.12}) \cdot (1 - \frac{{(k \cdot \frac{L}{r})}^{2}}{2 \cdot {C c}^{2}})

F_a - Allowable Stresses in Columns?f_y - Yield Strength of Steel?k - Effective Length Factor?L - Length of Bridge Column?r - Radius of Gyration?C_c - Slenderness Ratio Cc?

Allowable Stress when Slenderness Ratio is Less than Cc Example

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

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

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

103.184 = (\frac{250}{2.12}) \cdot (1 - \frac{{(0.5 \cdot \frac{3}{15})}^{2}}{2 \cdot 200^{2}})

103.184MPa = (\frac{250MPa}{2.12}) \cdot (1 - \frac{{(0.5 \cdot \frac{3m}{15mm})}^{2}}{2 \cdot 200^{2}})

103.184 = (\frac{250}{2.12}) \cdot (1 - \frac{{(0.5 \cdot \frac{3}{15})}^{2}}{2 \cdot 200^{2}})

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Allowable Stress when Slenderness Ratio is Less than Cc Solution

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

FIRST Step Consider the formula

F a = (\frac{f y}{2.12}) \cdot (1 - \frac{{(k \cdot \frac{L}{r})}^{2}}{2 \cdot {C c}^{2}})

Next Step Substitute values of Variables

∴

F a = (\frac{250MPa}{2.12}) \cdot (1 - \frac{{(0.5 \cdot \frac{3m}{15mm})}^{2}}{2 \cdot 200^{2}})

Next Step Convert Units

∴

F a = (\frac{250MPa}{2.12}) \cdot (1 - \frac{{(0.5 \cdot \frac{3m}{0.015m})}^{2}}{2 \cdot 200^{2}})

Next Step Prepare to Evaluate

∴

F a = (\frac{250}{2.12}) \cdot (1 - \frac{{(0.5 \cdot \frac{3}{0.015})}^{2}}{2 \cdot 200^{2}})

Next Step Evaluate

∴

F a = 103183962.264151Pa

Next Step Convert to Output's Unit

∴

F a = 103.183962264151MPa

LAST Step Rounding Answer

∴

F a = 103.184MPa

Allowable Stress when Slenderness Ratio is Less than Cc Formula Elements

Variables

Allowable Stresses in Columns

The allowable stresses in columns is the material failure stress (a property of the material) divided by a factor of safety greater than one.

Symbol: F_a

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Allowable Stresses in Columns

Yield Strength of Steel

Yield strength of steel is the level of stress that corresponds to the yield point.

Symbol: f_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Yield Strength 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

Length of Bridge Column

Length of bridge column is the distance between the two floors or the distance between the column's fixed points (fixed or pinned), where all its movement is constrained in all directions.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Bridge Column

Radius of Gyration

Radius of Gyration is used to compare how various structural shapes will behave under compression along an axis. It is used to predict buckling in a compression member or beam.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration

Slenderness Ratio Cc

Slenderness Ratio Cc is the ratio that demarcates between inelastic member buckling from elastic member buckling.

Symbol: C_c

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Slenderness Ratio Cc

Other Formulas to find Allowable Stresses in Columns

Go Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications

F a = \frac{π^{2} \cdot E}{2.12 \cdot {(k \cdot \frac{L}{r})}^{2}}

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

Allowable Stress when Slenderness Ratio is Less than Cc evaluator uses Allowable Stresses in Columns = (Yield Strength of Steel/2.12)*(1-((Effective Length Factor*Length of Bridge Column/Radius of Gyration)^2)/(2*Slenderness Ratio Cc^2)) to evaluate the Allowable Stresses in Columns, The Allowable Stress when Slenderness Ratio is Less than Cc formula is defined as the maximum stress a concentrically loaded column can take before failure. Allowable Stresses in Columns is denoted by F_a symbol.

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

FAQs on Allowable Stress when Slenderness Ratio is Less than Cc

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

The formula of Allowable Stress when Slenderness Ratio is Less than Cc is expressed as Allowable Stresses in Columns = (Yield Strength of Steel/2.12)*(1-((Effective Length Factor*Length of Bridge Column/Radius of Gyration)^2)/(2*Slenderness Ratio Cc^2)). Here is an example- 0.000103 = (250000000/2.12)*(1-((0.5*3/0.015)^2)/(2*200^2)).

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

With Yield Strength of Steel (f_y), Effective Length Factor (k), Length of Bridge Column (L), Radius of Gyration (r) & Slenderness Ratio Cc (C_c) we can find Allowable Stress when Slenderness Ratio is Less than Cc using the formula - Allowable Stresses in Columns = (Yield Strength of Steel/2.12)*(1-((Effective Length Factor*Length of Bridge Column/Radius of Gyration)^2)/(2*Slenderness Ratio Cc^2)).

What are the other ways to Calculate Allowable Stresses in Columns?

Here are the different ways to Calculate Allowable Stresses in Columns-

Allowable Stresses in Columns=(pi^2*Modulus of Elasticity)/(2.12*(Effective Length Factor*Length of Bridge Column/Radius of Gyration)^2)

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

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

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

Allowable Stress when Slenderness Ratio is Less than Cc is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Allowable Stress when Slenderness Ratio is Less than Cc can be measured.

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Allowable Stress when Slenderness Ratio is Less than Cc Formula

​GoAllowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications Formula

Allowable Stress when Slenderness Ratio is Less than Cc Example

Allowable Stress when Slenderness Ratio is Less than Cc Solution

Allowable Stress when Slenderness Ratio is Less than Cc Formula Elements

Other Formulas to find Allowable Stresses in Columns

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

FAQs on Allowable Stress when Slenderness Ratio is Less than Cc

Variable Name

GoAllowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications Formula