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Radius of Gyration given Effective Length and Crippling Load Formula

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Least radius of gyration of column is a critical parameter in structural engineering, representing the smallest radius of gyration among all possible axes of the column’s cross-section. Check FAQs

r = \sqrt{\frac{P cr \cdot {L e}^{2}}{π^{2} \cdot ε c \cdot A}}

r - Least Radius of Gyration of Column?P_cr - Column Crippling Load?L_e - Effective Length of Column?ε_c - Modulus of Elasticity of Column?A - Column Cross-Sectional Area?π - Archimedes' constant?

Radius of Gyration given Effective Length and Crippling Load Example

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Here is how the Radius of Gyration given Effective Length and Crippling Load equation looks like with Values.

Here is how the Radius of Gyration given Effective Length and Crippling Load equation looks like with Units.

Here is how the Radius of Gyration given Effective Length and Crippling Load equation looks like.

9.7953 = \sqrt{\frac{10000 \cdot 2500^{2}}{{3.1416}^{2} \cdot 10.56 \cdot 6.25}}

9.7953mm = \sqrt{\frac{10000N \cdot {2500mm}^{2}}{{3.1416}^{2} \cdot 10.56MPa \cdot 6.25m²}}

9.7953 = \sqrt{\frac{10000 \cdot 2500^{2}}{{3.1416}^{2} \cdot 10.56 \cdot 6.25}}

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Radius of Gyration given Effective Length and Crippling Load Solution

Follow our step by step solution on how to calculate Radius of Gyration given Effective Length and Crippling Load?

FIRST Step Consider the formula

r = \sqrt{\frac{P cr \cdot {L e}^{2}}{π^{2} \cdot ε c \cdot A}}

Next Step Substitute values of Variables

∴

r = \sqrt{\frac{10000N \cdot {2500mm}^{2}}{π^{2} \cdot 10.56MPa \cdot 6.25m²}}

Next Step Substitute values of Constants

∴

r = \sqrt{\frac{10000N \cdot {2500mm}^{2}}{{3.1416}^{2} \cdot 10.56MPa \cdot 6.25m²}}

Next Step Convert Units

∴

r = \sqrt{\frac{10000N \cdot {2.5m}^{2}}{{3.1416}^{2} \cdot 1.1E+7Pa \cdot 6.25m²}}

Next Step Prepare to Evaluate

∴

r = \sqrt{\frac{10000 \cdot {2.5}^{2}}{{3.1416}^{2} \cdot 1.1E+7 \cdot 6.25}}

Next Step Evaluate

∴

r = 0.00979530962095613m

Next Step Convert to Output's Unit

∴

r = 9.79530962095613mm

LAST Step Rounding Answer

∴

r = 9.7953mm

Radius of Gyration given Effective Length and Crippling Load Formula Elements

Variables

Constants

Functions

Least Radius of Gyration of Column

Least radius of gyration of column is a critical parameter in structural engineering, representing the smallest radius of gyration among all possible axes of the column’s cross-section.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Least Radius of Gyration of Column

Column Crippling Load

Column crippling load also known as the buckling load, is the maximum axial compressive load that a column can withstand before it buckles or fails due to instability.

Symbol: P_cr

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Column Crippling Load

Effective Length of Column

Effective length of column is the length of an equivalent pin-ended column that has the same load-carrying capacity as the actual column under consideration.

Symbol: L_e

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Modulus of Elasticity of Column

Modulus of elasticity of column also known as Young’s modulus, is a measure of a material’s stiffness or rigidity which quantifies the relationship between stress and strain.

Symbol: ε_c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity of Column

Column Cross-Sectional Area

Column cross-sectional area is a geometric property that represents the area of the column’s cross-section, is crucial for calculating the axial stresses and the load-carrying capacity of the column.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Column Cross-Sectional Area

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

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 Estimation of Effective Length of Columns category

Go Effective Length of Column given Actual Length if Both Ends of Column are Fixed

L e = \frac{L}{2}

Go Effective Length of Column given Actual Length if One End is Fixed Other is Free

L e = 2 \cdot L

Go Effective Length of Column given Actual Length if One End is Fixed Other is Hinged

L e = \frac{L}{\sqrt{2}}

Go Effective Length of Column given Crippling Load for any type of End Condition

L e = \sqrt{\frac{π^{2} \cdot ε c \cdot I}{P cr}}

How to Evaluate Radius of Gyration given Effective Length and Crippling Load?

Radius of Gyration given Effective Length and Crippling Load evaluator uses Least Radius of Gyration of Column = sqrt((Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column*Column Cross-Sectional Area)) to evaluate the Least Radius of Gyration of Column, Radius of Gyration given Effective Length and Crippling Load formula is defined as a measure of the distribution of the stiffness of a column around its axis, which is essential in determining the column's resistance to buckling under compressive loads, providing valuable insights into the structural integrity of the column. Least Radius of Gyration of Column is denoted by r symbol.

How to evaluate Radius of Gyration given Effective Length and Crippling Load using this online evaluator? To use this online evaluator for Radius of Gyration given Effective Length and Crippling Load, enter Column Crippling Load (P_cr), Effective Length of Column (L_e), Modulus of Elasticity of Column (ε_c) & Column Cross-Sectional Area (A) and hit the calculate button.

FAQs on Radius of Gyration given Effective Length and Crippling Load

What is the formula to find Radius of Gyration given Effective Length and Crippling Load?

The formula of Radius of Gyration given Effective Length and Crippling Load is expressed as Least Radius of Gyration of Column = sqrt((Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column*Column Cross-Sectional Area)). Here is an example- 9795.31 = sqrt((10000*2.5^2)/(pi^2*10560000*6.25)).

How to calculate Radius of Gyration given Effective Length and Crippling Load?

With Column Crippling Load (P_cr), Effective Length of Column (L_e), Modulus of Elasticity of Column (ε_c) & Column Cross-Sectional Area (A) we can find Radius of Gyration given Effective Length and Crippling Load using the formula - Least Radius of Gyration of Column = sqrt((Column Crippling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity of Column*Column Cross-Sectional Area)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Radius of Gyration given Effective Length and Crippling Load be negative?

No, the Radius of Gyration given Effective Length and Crippling Load, measured in Length cannot be negative.

Which unit is used to measure Radius of Gyration given Effective Length and Crippling Load?

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

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Radius of Gyration given Effective Length and Crippling Load Formula

Radius of Gyration given Effective Length and Crippling Load Example

Radius of Gyration given Effective Length and Crippling Load Solution

Radius of Gyration given Effective Length and Crippling Load Formula Elements

Other formulas in Estimation of Effective Length of Columns category

How to Evaluate Radius of Gyration given Effective Length and Crippling Load?

FAQs on Radius of Gyration given Effective Length and Crippling Load

Variable Name