Radius of Gyration given Effective Length and Crippling Load Calculator

✖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.ⓘ Column Crippling Load [P_cr]			+10% -10%
✖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.ⓘ Effective Length of Column [L_e]			+10% -10%
✖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.ⓘ Modulus of Elasticity of Column [ε_c]			+10% -10%
✖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.ⓘ Column Cross-Sectional Area [A]			+10% -10%

✖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.ⓘ Radius of Gyration given Effective Length and Crippling Load [r]

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Radius of Gyration given Effective Length and Crippling Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
r = sqrt((P_cr*L_e^2)/(pi^2*ε_c*A))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Least Radius of Gyration of Column - (Measured in Meter) - 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.
Column Crippling Load - (Measured in Newton) - 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.
Effective Length of Column - (Measured in Meter) - 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.
Modulus of Elasticity of Column - (Measured in Pascal) - 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.
Column Cross-Sectional Area - (Measured in Square Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Column Crippling Load: 10000 Newton --> 10000 Newton No Conversion Required
Effective Length of Column: 2500 Millimeter --> 2.5 Meter (Check conversion here)
Modulus of Elasticity of Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Column Cross-Sectional Area: 6.25 Square Meter --> 6.25 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = sqrt((P_cr*L_e^2)/(pi^2*ε_c*A)) --> sqrt((10000*2.5^2)/(pi^2*10560000*6.25))

Evaluating ... ...

r = 0.00979530962095613

STEP 3: Convert Result to Output's Unit

0.00979530962095613 Meter -->9.79530962095613 Millimeter (Check conversion here)

FINAL ANSWER

9.79530962095613 ≈ 9.79531 Millimeter <-- Least Radius of Gyration of Column

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Estimation of Effective Length of Columns Calculators

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

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< Effective Length Calculators

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

LaTeX Go Effective Length of Column = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load))

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

LaTeX Go Effective Length of Column = Length of Column/(sqrt(2))

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

LaTeX Go Effective Length of Column = 2*Length of Column

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

LaTeX Go Effective Length of Column = Length of Column/2

Radius of Gyration given Effective Length and Crippling Load Formula

LaTeX Go

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))
r = sqrt((P_cr*L_e^2)/(pi^2*ε_c*A))

What is meant by Effective Length of a Column also define Slenderness Ratio?

The effective length of the column is the length of an equivalent column of the same material and cross sectional area with hinged ends and having the value of the crippling load equal to that of the given column. The least radius of gyration is the radius of gyration where the least moment of inertia is considered.

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

Radius of Gyration given Effective Length and Crippling Load calculator 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 calculate 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 calculate Radius of Gyration given Effective Length and Crippling Load using this online calculator? To use this online calculator 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. Here is how the Radius of Gyration given Effective Length and Crippling Load calculation can be explained with given input values -> 9795.31 = sqrt((10000*2.5^2)/(pi^2*10560000*6.25)).

FAQ

What is Radius of Gyration given Effective Length and Crippling Load?

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 and is represented as r = sqrt((P_cr*L_e^2)/(pi^2*ε_c*A)) or 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)). 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, 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, 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 & 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.

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

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 is calculated using 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 calculate Radius of Gyration given Effective Length and Crippling Load, you need Column Crippling Load (P_cr), Effective Length of Column (L_e), Modulus of Elasticity of Column (ε_c) & Column Cross-Sectional Area (A). With our tool, you need to enter the respective value for Column Crippling Load, Effective Length of Column, Modulus of Elasticity of Column & Column Cross-Sectional Area and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Least Radius of Gyration of Column?

In this formula, Least Radius of Gyration of Column uses Column Crippling Load, Effective Length of Column, Modulus of Elasticity of Column & Column Cross-Sectional Area. We can use 1 other way(s) to calculate the same, which is/are as follows -

Least Radius of Gyration of Column = Length of Column/Slenderness Ratio

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