Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 given Critical Buckling Load for Pin Ended Columns by Euler's Formula [r_gyration]

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Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula

Formula

`"r"_{"gyration "} = sqrt(("P"_{"Buckling Load"}*"L"^2)/(pi^2*"E"*"A"))`

Example

`"11.41359mm"=sqrt(("5N"*("3000mm")^2)/(pi^2*"50MPa"*"700mm²"))`

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Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 00.004 seconds)

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Home » Engineering » Civil » Columns » Elastic Flexural Buckling of Columns » Pin-Ended Columns » Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula

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< 4 Pin-Ended Columns Calculators

Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula

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 Critical Buckling Load for Pin Ended Columns by Euler's Formula

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

Critical Buckling Load for Pin Ended Columns by Euler's Formula

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 Critical Buckling Load for Pin Ended Columns by Euler's Formula

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

Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula Formula

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))

What is Critical Buckling Load?

Buckling is a sudden lateral failure of an axially loaded member in compression, under a load value less than the compressive load-carrying capacity of that member. The axial compression load corresponding to this mode of failure is referred to as critical buckling load.

What does Buckling mean?

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 given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 given Critical Buckling Load for Pin Ended Columns by Euler's Formula is defined as as a function of slenderness ratio, elastic modulus of column and column cross-sectional area. Radius of Gyration of Column is denoted by r_gyration symbol.

How to calculate Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula using this online calculator? To use this online calculator for Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula, 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 given Critical Buckling Load for Pin Ended Columns by Euler's Formula 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 given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

The Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula is defined as as a function of slenderness ratio, elastic modulus of column and column cross-sectional area 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 given Critical Buckling Load for Pin Ended Columns by Euler's Formula?

The Radius of Gyration given Critical Buckling Load for Pin Ended Columns by Euler's Formula is defined as as a function of slenderness ratio, elastic modulus of column and column cross-sectional area 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 given Critical Buckling Load for Pin Ended Columns by Euler's Formula, 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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