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Rankine's Constant Formula

GoRankine's Constant given Crippling Load Formula

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Rankine's Constant is the constant of Rankine's empirical formula. Check FAQs

α = \frac{σ c}{π^{2} \cdot E}

α - Rankine's Constant?σ_c - Column Crushing Stress?E - Modulus of Elasticity Column?π - Archimedes' constant?

Rankine's Constant Example

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Here is how the Rankine's Constant equation looks like with Values.

Here is how the Rankine's Constant equation looks like with Units.

Here is how the Rankine's Constant equation looks like.

0.0004 = \frac{750}{{3.1416}^{2} \cdot 200000}

0.0004 = \frac{750MPa}{{3.1416}^{2} \cdot 200000MPa}

0.0004 = \frac{750}{{3.1416}^{2} \cdot 200000}

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Rankine's Constant Solution

Follow our step by step solution on how to calculate Rankine's Constant?

FIRST Step Consider the formula

α = \frac{σ c}{π^{2} \cdot E}

Next Step Substitute values of Variables

∴

α = \frac{750MPa}{π^{2} \cdot 200000MPa}

Next Step Substitute values of Constants

∴

α = \frac{750MPa}{{3.1416}^{2} \cdot 200000MPa}

Next Step Convert Units

∴

α = \frac{7.5E+8Pa}{{3.1416}^{2} \cdot 2E+11Pa}

Next Step Prepare to Evaluate

∴

α = \frac{7.5E+8}{{3.1416}^{2} \cdot 2E+11}

Next Step Evaluate

∴

α = 0.000379954438658767

LAST Step Rounding Answer

∴

α = 0.0004

Rankine's Constant Formula Elements

Variables

Constants

Rankine's Constant

Rankine's Constant is the constant of Rankine's empirical formula.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Rankine's Constant

Column Crushing Stress

Column Crushing Stress is a special type of localized compressive stress which occurs at the surface of contact of two members that are relatively at rest.

Symbol: σ_c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Column Crushing Stress

Modulus of Elasticity Column

Modulus of Elasticity Column is a quantity that measures column's resistance to being deformed elastically when stress is applied to it.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity Column

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 Rankine's Constant

Go Rankine's Constant given Crippling Load

α = (\frac{σ c \cdot A}{P} - 1) \cdot {(\frac{r least}{L eff})}^{2}

Other formulas in Euler and Rankine's Theory category

Go Crippling Load by Rankine's

P r = \frac{P c \cdot P E}{P c + P E}

Go Crippling Load given Rankine's Constant

P = \frac{σ c \cdot A}{1 + α \cdot {(\frac{L eff}{r least})}^{2}}

Go Cross-Sectional Area of Column given Crippling Load and Rankine's Constant

A = \frac{P \cdot (1 + α \cdot {(\frac{L eff}{r least})}^{2})}{σ c}

Go Cross-Sectional Area of Column given Crushing Load

A = \frac{P c}{σ c}

How to Evaluate Rankine's Constant?

Rankine's Constant evaluator uses Rankine's Constant = Column Crushing Stress/(pi^2*Modulus of Elasticity Column) to evaluate the Rankine's Constant, The Rankine's Constant formula is defined as a fundamental value in the Euler and Rankine's Theory, representing the relationship between the critical stress of a column and its modulus of elasticity, providing a crucial parameter in structural analysis and engineering design. Rankine's Constant is denoted by α symbol.

How to evaluate Rankine's Constant using this online evaluator? To use this online evaluator for Rankine's Constant, enter Column Crushing Stress (σ_c) & Modulus of Elasticity Column (E) and hit the calculate button.

FAQs on Rankine's Constant

What is the formula to find Rankine's Constant?

The formula of Rankine's Constant is expressed as Rankine's Constant = Column Crushing Stress/(pi^2*Modulus of Elasticity Column). Here is an example- 0.00038 = 750000000/(pi^2*200000000000).

How to calculate Rankine's Constant?

With Column Crushing Stress (σ_c) & Modulus of Elasticity Column (E) we can find Rankine's Constant using the formula - Rankine's Constant = Column Crushing Stress/(pi^2*Modulus of Elasticity Column). This formula also uses Archimedes' constant .

What are the other ways to Calculate Rankine's Constant?

Here are the different ways to Calculate Rankine's Constant-

Rankine's Constant=((Column Crushing Stress*Column Cross Sectional Area)/Crippling Load-1)*((Least Radius of Gyration Column)/Effective Column Length)^2

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Rankine's Constant Formula

​GoRankine's Constant given Crippling Load Formula

Rankine's Constant Example

Rankine's Constant Solution

Rankine's Constant Formula Elements

Other Formulas to find Rankine's Constant

Other formulas in Euler and Rankine's Theory category

How to Evaluate Rankine's Constant?

FAQs on Rankine's Constant

Variable Name

GoRankine's Constant given Crippling Load Formula