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Effective Length of Column given Crippling Load and Rankine's Constant Formula

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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. Check FAQs

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

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

Effective Length of Column given Crippling Load and Rankine's Constant Example

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Here is how the Effective Length of Column given Crippling Load and Rankine's Constant equation looks like with Values.

Here is how the Effective Length of Column given Crippling Load and Rankine's Constant equation looks like with Units.

Here is how the Effective Length of Column given Crippling Load and Rankine's Constant equation looks like.

3000.0001 = \sqrt{(750 \cdot \frac{2000}{588.9524} - 1) \cdot \frac{{47.02}^{2}}{0.0004}}

3000.0001mm = \sqrt{(750MPa \cdot \frac{2000mm²}{588.9524kN} - 1) \cdot \frac{{47.02mm}^{2}}{0.0004}}

3000.0001 = \sqrt{(750 \cdot \frac{2000}{588.9524} - 1) \cdot \frac{{47.02}^{2}}{0.0004}}

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Effective Length of Column given Crippling Load and Rankine's Constant Solution

Follow our step by step solution on how to calculate Effective Length of Column given Crippling Load and Rankine's Constant?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

L eff = \sqrt{(7.5E+8Pa \cdot \frac{0.002m²}{588952.4N} - 1) \cdot \frac{{0.047m}^{2}}{0.0004}}

Next Step Prepare to Evaluate

∴

L eff = \sqrt{(7.5E+8 \cdot \frac{0.002}{588952.4} - 1) \cdot \frac{{0.047}^{2}}{0.0004}}

Next Step Evaluate

∴

L eff = 3.00000005533691m

Next Step Convert to Output's Unit

∴

L eff = 3000.00005533691mm

LAST Step Rounding Answer

∴

L eff = 3000.0001mm

Effective Length of Column given Crippling Load and Rankine's Constant Formula Elements

Variables

Functions

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

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

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 Effective Length of Column given Crippling Load and Rankine's Constant?

Effective Length of Column given Crippling Load and Rankine's Constant evaluator uses Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant) to evaluate the Effective Column Length, The Effective Length of Column given Crippling Load and Rankine's Constant formula is defined as a measure of the reduced length of a column that takes into account the crippling load and Rankine's constant, providing a more accurate representation of the column's behavior under compressive loads in structural analysis. Effective Column Length is denoted by L_eff symbol.

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

FAQs on Effective Length of Column given Crippling Load and Rankine's Constant

What is the formula to find Effective Length of Column given Crippling Load and Rankine's Constant?

The formula of Effective Length of Column given Crippling Load and Rankine's Constant is expressed as Effective Column Length = sqrt((Column Crushing Stress*Column Cross Sectional Area/Crippling Load-1)*(Least Radius of Gyration Column^2)/Rankine's Constant). Here is an example- 3E+6 = sqrt((750000000*0.002/588952.4-1)*(0.04702^2)/0.00038).

How to calculate Effective Length of Column given Crippling Load and Rankine's Constant?

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

Can the Effective Length of Column given Crippling Load and Rankine's Constant be negative?

No, the Effective Length of Column given Crippling Load and Rankine's Constant, measured in Length cannot be negative.

Which unit is used to measure Effective Length of Column given Crippling Load and Rankine's Constant?

Effective Length of Column 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 Effective Length of Column given Crippling Load and Rankine's Constant can be measured.

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Effective Length of Column given Crippling Load and Rankine's Constant Formula

Effective Length of Column given Crippling Load and Rankine's Constant Example

Effective Length of Column given Crippling Load and Rankine's Constant Solution

Effective Length of Column given Crippling Load and Rankine's Constant Formula Elements

Other formulas in Euler and Rankine's Theory category

How to Evaluate Effective Length of Column given Crippling Load and Rankine's Constant?

FAQs on Effective Length of Column given Crippling Load and Rankine's Constant

Variable Name