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

GoAllowable Stress when Slenderness Ratio is Less than Cc 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{π^{2} \cdot E}{2.12 \cdot {(k \cdot \frac{L}{r})}^{2}}

F_a - Allowable Stresses in Columns?E - Modulus of Elasticity?k - Effective Length Factor?L - Length of Bridge Column?r - Radius of Gyration?π - Archimedes' constant?

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

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Here is how the Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications equation looks like with Values.

Here is how the Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications equation looks like with Units.

Here is how the Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications equation looks like.

0.0233 = \frac{{3.1416}^{2} \cdot 50}{2.12 \cdot {(0.5 \cdot \frac{3}{15})}^{2}}

0.0233MPa = \frac{{3.1416}^{2} \cdot 50MPa}{2.12 \cdot {(0.5 \cdot \frac{3m}{15mm})}^{2}}

0.0233 = \frac{{3.1416}^{2} \cdot 50}{2.12 \cdot {(0.5 \cdot \frac{3}{15})}^{2}}

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

Follow our step by step solution on how to calculate Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F a = \frac{π^{2} \cdot 50MPa}{2.12 \cdot {(0.5 \cdot \frac{3m}{15mm})}^{2}}

Next Step Substitute values of Constants

∴

F a = \frac{{3.1416}^{2} \cdot 50MPa}{2.12 \cdot {(0.5 \cdot \frac{3m}{15mm})}^{2}}

Next Step Convert Units

∴

F a = \frac{{3.1416}^{2} \cdot 50MPa}{2.12 \cdot {(0.5 \cdot \frac{3m}{0.015m})}^{2}}

Next Step Prepare to Evaluate

∴

F a = \frac{{3.1416}^{2} \cdot 50}{2.12 \cdot {(0.5 \cdot \frac{3}{0.015})}^{2}}

Next Step Evaluate

∴

F a = 23277.3688704938Pa

Next Step Convert to Output's Unit

∴

F a = 0.0232773688704938MPa

LAST Step Rounding Answer

∴

F a = 0.0233MPa

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

Variables

Constants

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

Modulus of Elasticity

The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.

Symbol: E

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

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

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 Stresses in Columns

Go Allowable Stress when Slenderness Ratio is Less than Cc

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

How to Evaluate Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications?

Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications evaluator uses Allowable Stresses in Columns = (pi^2*Modulus of Elasticity)/(2.12*(Effective Length Factor*Length of Bridge Column/Radius of Gyration)^2) to evaluate the Allowable Stresses in Columns, The Allowable Stresses in Concentrically loaded Columns based on AASHTO Bridge Design Specifications (Braced Column) formula is defined as the maximum allowable stress a concentrically column can take before failure. Allowable Stresses in Columns is denoted by F_a symbol.

How to evaluate Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications using this online evaluator? To use this online evaluator for Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications, enter Modulus of Elasticity (E), Effective Length Factor (k), Length of Bridge Column (L) & Radius of Gyration (r) and hit the calculate button.

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

What is the formula to find Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications?

The formula of Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications is expressed as Allowable Stresses in Columns = (pi^2*Modulus of Elasticity)/(2.12*(Effective Length Factor*Length of Bridge Column/Radius of Gyration)^2). Here is an example- 2.3E-8 = (pi^2*50000000)/(2.12*(0.5*3/0.015)^2).

How to calculate Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications?

With Modulus of Elasticity (E), Effective Length Factor (k), Length of Bridge Column (L) & Radius of Gyration (r) we can find Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications using the formula - Allowable Stresses in Columns = (pi^2*Modulus of Elasticity)/(2.12*(Effective Length Factor*Length of Bridge Column/Radius of Gyration)^2). This formula also uses Archimedes' constant .

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=(Yield Strength of Steel/2.12)*(1-((Effective Length Factor*Length of Bridge Column/Radius of Gyration)^2)/(2*Slenderness Ratio Cc^2))

Can the Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications be negative?

No, the Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications, measured in Stress cannot be negative.

Which unit is used to measure Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications?

Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications 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 Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications can be measured.

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

​GoAllowable Stress when Slenderness Ratio is Less than Cc Formula

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

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

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

Other Formulas to find Allowable Stresses in Columns

How to Evaluate Allowable Stresses in Concentrically Loaded Columns based on AASHTO Bridge Design Specifications?

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

Variable Name

GoAllowable Stress when Slenderness Ratio is Less than Cc Formula