Radius of Gyration of Column given Elastic Critical Buckling Load Calculator

✖The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity.ⓘ Buckling Load [P_{Buckling Load}]			+10% -10%
✖The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.ⓘ Effective Length of Column [L]			+10% -10%
✖The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.ⓘ Modulus of Elasticity [E]			+10% -10%
✖Column Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point.ⓘ Column Cross-Sectional Area [A]			+10% -10%

✖The Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.ⓘ Radius of Gyration of Column given Elastic Critical Buckling Load [r_gyration]

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Radius of Gyration of Column given Elastic Critical Buckling Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Gyration of Column = sqrt((Buckling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity*Column Cross-Sectional Area))
r_gyration = sqrt((P_{Buckling Load}*L^2)/(pi^2*E*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

Radius of Gyration of Column - (Measured in Millimeter) - The Radius of Gyration of Column about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass.
Buckling Load - (Measured in Newton) - The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity.
Effective Length of Column - (Measured in Millimeter) - The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration.
Modulus of Elasticity - (Measured in Megapascal) - The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality.
Column Cross-Sectional Area - (Measured in Square Millimeter) - Column Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point.

STEP 1: Convert Input(s) to Base Unit

Buckling Load: 5 Newton --> 5 Newton No Conversion Required
Effective Length of Column: 3000 Millimeter --> 3000 Millimeter No Conversion Required
Modulus of Elasticity: 50 Megapascal --> 50 Megapascal No Conversion Required
Column Cross-Sectional Area: 700 Square Millimeter --> 700 Square Millimeter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_gyration = sqrt((P_{Buckling Load}*L^2)/(pi^2*E*A)) --> sqrt((5*3000^2)/(pi^2*50*700))

Evaluating ... ...

r_gyration = 11.4135924780252

STEP 3: Convert Result to Output's Unit

0.0114135924780252 Meter -->11.4135924780252 Millimeter (Check conversion here)

FINAL ANSWER

11.4135924780252 ≈ 11.41359 Millimeter <-- Radius of Gyration of Column

(Calculation completed in 00.007 seconds)

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Created by Rudrani Tidke

Cummins College of Engineering for Women (CCEW), Pune

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< Slender Columns Calculators

Radius of Gyration of Column given Elastic Critical Buckling Load

LaTeX Go Radius of Gyration of Column = sqrt((Buckling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity*Column Cross-Sectional Area))

Cross-Sectional Area given Elastic Critical Buckling Load

LaTeX Go Column Cross-Sectional Area = (Buckling Load*(Effective Length of Column/Radius of Gyration of Column)^2)/(pi^2*Modulus of Elasticity)

Elastic Critical Buckling Load

LaTeX Go Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2

Slenderness Ratio given Elastic Critical Buckling Load

LaTeX Go Slenderness Ratio = sqrt((pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/Buckling Load)

Radius of Gyration of Column given Elastic Critical Buckling Load Formula

LaTeX Go

Radius of Gyration of Column = sqrt((Buckling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity*Column Cross-Sectional Area))
r_gyration = sqrt((P_{Buckling Load}*L^2)/(pi^2*E*A))

Column End Conditions for Effective Length of Column

The coefficient n accounts for end conditions.
When the column is pivoted at both ends, n = 1;
when one end is fixed and the other end is rounded, n = 0.7;
when both ends are fixed, n = 0.5; and
when one end is fixed and the other is free, n = 2.

Define Buckling.

In structural engineering, buckling is the sudden change in shape (deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear.

How to Calculate Radius of Gyration of Column given Elastic Critical Buckling Load?

Radius of Gyration of Column given Elastic Critical Buckling Load calculator uses Radius of Gyration of Column = sqrt((Buckling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity*Column Cross-Sectional Area)) to calculate the Radius of Gyration of Column, The Radius of Gyration of Column given Elastic Critical Buckling Load formula is defined as the length used to describe the distribution of cross-sectional area in a column around its centroidal axis. Radius of Gyration of Column is denoted by r_gyration symbol.

How to calculate Radius of Gyration of Column given Elastic Critical Buckling Load using this online calculator? To use this online calculator for Radius of Gyration of Column given Elastic Critical Buckling Load, enter Buckling Load (P_{Buckling Load}), Effective Length of Column (L), Modulus of Elasticity (E) & Column Cross-Sectional Area (A) and hit the calculate button. Here is how the Radius of Gyration of Column given Elastic Critical Buckling Load calculation can be explained with given input values -> 11.41359 = sqrt((5*3^2)/(pi^2*50000000*0.0007)).

FAQ

What is Radius of Gyration of Column given Elastic Critical Buckling Load?

The Radius of Gyration of Column given Elastic Critical Buckling Load formula is defined as the length used to describe the distribution of cross-sectional area in a column around its centroidal axis and is represented as r_gyration = sqrt((P_{Buckling Load}*L^2)/(pi^2*E*A)) or Radius of Gyration of Column = sqrt((Buckling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity*Column Cross-Sectional Area)). The Buckling Load is the load at which the column starts buckling. The buckling load of a given material depends on the Slenderness ratio, Area of a cross-section, and Modulus of Elasticity, The Effective Length of Column can be defined as the length of an equivalent pin-ended column having the same load-carrying capacity as the member under consideration, The Modulus of Elasticity is the measure of the stiffness of a material. It is the slope of stress and strain diagram up to the limit of proportionality & Column Cross-Sectional Area is the area of a two-dimensional shape that is obtained when a three-dimensional object is sliced perpendicular to some specified axis at a point.

How to calculate Radius of Gyration of Column given Elastic Critical Buckling Load?

The Radius of Gyration of Column given Elastic Critical Buckling Load formula is defined as the length used to describe the distribution of cross-sectional area in a column around its centroidal axis is calculated using Radius of Gyration of Column = sqrt((Buckling Load*Effective Length of Column^2)/(pi^2*Modulus of Elasticity*Column Cross-Sectional Area)). To calculate Radius of Gyration of Column given Elastic Critical Buckling Load, you need Buckling Load (P_{Buckling Load}), Effective Length of Column (L), Modulus of Elasticity (E) & Column Cross-Sectional Area (A). With our tool, you need to enter the respective value for Buckling Load, Effective Length of Column, Modulus of Elasticity & 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.

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