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Rankine'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 \cdot A}{P} - 1) \cdot {(\frac{r least}{L eff})}^{2}

α - Rankine's Constant?σ_c - Column Crushing Stress?A - Column Cross Sectional Area?P - Crippling Load?r_least - Least Radius of Gyration Column?L_eff - Effective Column Length?

Rankine's Constant given Crippling Load Example

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

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

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

0.0004 = (\frac{750 \cdot 2000}{588.9524} - 1) \cdot {(\frac{47.02}{3000})}^{2}

0.0004 = (\frac{750MPa \cdot 2000mm²}{588.9524kN} - 1) \cdot {(\frac{47.02mm}{3000mm})}^{2}

0.0004 = (\frac{750 \cdot 2000}{588.9524} - 1) \cdot {(\frac{47.02}{3000})}^{2}

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Rankine's Constant given Crippling Load Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

α = (\frac{750MPa \cdot 2000mm²}{588.9524kN} - 1) \cdot {(\frac{47.02mm}{3000mm})}^{2}

Next Step Convert Units

∴

α = (\frac{7.5E+8Pa \cdot 0.002m²}{588952.4N} - 1) \cdot {(\frac{0.047m}{3m})}^{2}

Next Step Prepare to Evaluate

∴

α = (\frac{7.5E+8 \cdot 0.002}{588952.4} - 1) \cdot {(\frac{0.047}{3})}^{2}

Next Step Evaluate

∴

α = 0.000380000014018684

LAST Step Rounding Answer

∴

α = 0.0004

Rankine's Constant given Crippling Load Formula Elements

Variables

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

Column Cross Sectional Area

Column Cross Sectional Area is the area of a two-dimensional shape that is obtained when a three dimensional shape is sliced perpendicular to some specified axis at a point.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Column Cross Sectional Area

Crippling Load

Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Symbol: P

Measurement: ForceUnit: kN

Note: Value should be greater than 0.

Formulas to find Crippling Load

Least Radius of Gyration Column

Least Radius of Gyration Column is the smallest value of the radius of gyration is used for structural calculations.

Symbol: r_least

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Least Radius of Gyration Column

Effective Column Length

Effective Column Length can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.

Symbol: L_eff

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Column Length

Other Formulas to find Rankine's Constant

Go Rankine's Constant

α = \frac{σ c}{π^{2} \cdot E}

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 given Crippling Load?

Rankine's Constant given Crippling Load evaluator uses Rankine's Constant = ((Column Crushing Stress*Column Cross Sectional Area)/Crippling Load-1)*((Least Radius of Gyration Column)/Effective Column Length)^2 to evaluate the Rankine's Constant, The Rankine's Constant given Crippling Load formula is defined as a measure of the critical load at which a long slender column will buckle, considering the crippling load, cross-sectional area, and effective length of the column, providing a crucial parameter in Euler and Rankine's Theory for structural analysis. Rankine's Constant is denoted by α symbol.

How to evaluate Rankine's Constant given Crippling Load using this online evaluator? To use this online evaluator for Rankine's Constant given Crippling Load, enter Column Crushing Stress (σ_c), Column Cross Sectional Area (A), Crippling Load (P), Least Radius of Gyration Column (r_least) & Effective Column Length (L_eff) and hit the calculate button.

FAQs on Rankine's Constant given Crippling Load

What is the formula to find Rankine's Constant given Crippling Load?

The formula of Rankine's Constant given Crippling Load is expressed as Rankine's Constant = ((Column Crushing Stress*Column Cross Sectional Area)/Crippling Load-1)*((Least Radius of Gyration Column)/Effective Column Length)^2. Here is an example- 0.00038 = ((750000000*0.002)/588952.4-1)*((0.04702)/3)^2.

How to calculate Rankine's Constant given Crippling Load?

With Column Crushing Stress (σ_c), Column Cross Sectional Area (A), Crippling Load (P), Least Radius of Gyration Column (r_least) & Effective Column Length (L_eff) we can find Rankine's Constant given Crippling Load using the formula - Rankine's Constant = ((Column Crushing Stress*Column Cross Sectional Area)/Crippling Load-1)*((Least Radius of Gyration Column)/Effective Column Length)^2.

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/(pi^2*Modulus of Elasticity Column)

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Rankine's Constant given Crippling Load Formula

​GoRankine's Constant Formula

Rankine's Constant given Crippling Load Example

Rankine's Constant given Crippling Load Solution

Rankine's Constant given Crippling Load Formula Elements

Other Formulas to find Rankine's Constant

Other formulas in Euler and Rankine's Theory category

How to Evaluate Rankine's Constant given Crippling Load?

FAQs on Rankine's Constant given Crippling Load

Variable Name

GoRankine's Constant Formula