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Least Radius of Gyration given Crippling Load and Rankine's Constant Formula

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

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

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

Least Radius of Gyration given Crippling Load and Rankine's Constant Example

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Here is how the Least Radius of Gyration given Crippling Load and Rankine's Constant equation looks like with Values.

Here is how the Least Radius of Gyration given Crippling Load and Rankine's Constant equation looks like with Units.

Here is how the Least Radius of Gyration given Crippling Load and Rankine's Constant equation looks like.

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

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

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

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Least Radius of Gyration given Crippling Load and Rankine's Constant Solution

Follow our step by step solution on how to calculate Least Radius of Gyration given Crippling Load and Rankine's Constant?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r least = \sqrt{\frac{0.0004 \cdot {3000mm}^{2}}{750MPa \cdot \frac{2000mm²}{588.9524kN} - 1}}

Next Step Convert Units

∴

r least = \sqrt{\frac{0.0004 \cdot {3m}^{2}}{7.5E+8Pa \cdot \frac{0.002m²}{588952.4N} - 1}}

Next Step Prepare to Evaluate

∴

r least = \sqrt{\frac{0.0004 \cdot 3^{2}}{7.5E+8 \cdot \frac{0.002}{588952.4} - 1}}

Next Step Evaluate

∴

r least = 0.0470199991326862m

Next Step Convert to Output's Unit

∴

r least = 47.0199991326862mm

LAST Step Rounding Answer

∴

r least = 47.02mm

Least Radius of Gyration given Crippling Load and Rankine's Constant Formula Elements

Variables

Functions

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

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

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Least Radius of Gyration given Crippling Load and Rankine's Constant?

Least Radius of Gyration given Crippling Load and Rankine's Constant evaluator uses Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)) to evaluate the Least Radius of Gyration Column, The Least Radius of Gyration given Crippling Load and Rankine's Constant formula is defined as a measure that determines the minimum radius of gyration of a column under a crippling load, considering the effective length, cross-sectional area, and crippling stress, which is essential in Euler and Rankine's theory of column design. Least Radius of Gyration Column is denoted by r_least symbol.

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

FAQs on Least Radius of Gyration given Crippling Load and Rankine's Constant

What is the formula to find Least Radius of Gyration given Crippling Load and Rankine's Constant?

The formula of Least Radius of Gyration given Crippling Load and Rankine's Constant is expressed as Least Radius of Gyration Column = sqrt((Rankine's Constant*Effective Column Length^2)/(Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)). Here is an example- 47020 = sqrt((0.00038*3^2)/(750000000*0.002/588952.4-1)).

How to calculate Least Radius of Gyration given Crippling Load and Rankine's Constant?

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

Can the Least Radius of Gyration given Crippling Load and Rankine's Constant be negative?

No, the Least Radius of Gyration given Crippling Load and Rankine's Constant, measured in Length cannot be negative.

Which unit is used to measure Least Radius of Gyration given Crippling Load and Rankine's Constant?

Least Radius of Gyration given Crippling Load and Rankine's Constant is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Least Radius of Gyration given Crippling Load and Rankine's Constant can be measured.

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Least Radius of Gyration given Crippling Load and Rankine's Constant Formula

Least Radius of Gyration given Crippling Load and Rankine's Constant Example

Least Radius of Gyration given Crippling Load and Rankine's Constant Solution

Least Radius of Gyration given Crippling Load and Rankine's Constant Formula Elements

Other formulas in Euler and Rankine's Theory category

How to Evaluate Least Radius of Gyration given Crippling Load and Rankine's Constant?

FAQs on Least Radius of Gyration given Crippling Load and Rankine's Constant

Variable Name