FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Elastic Critical Buckling Load Formula

Fx Copy

LaTeX Copy

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. Check FAQs

P Buckling Load = \frac{π^{2} \cdot E \cdot A}{{(\frac{L}{r gyration})}^{2}}

P_{Buckling Load} - Buckling Load?E - Modulus of Elasticity?A - Column Cross-Sectional Area?L - Effective Length of Column?r_gyration - Radius of Gyration of Column?π - Archimedes' constant?

Elastic Critical Buckling Load Example

With values

With units

Only example

Here is how the Elastic Critical Buckling Load equation looks like with Values.

Here is how the Elastic Critical Buckling Load equation looks like with Units.

Here is how the Elastic Critical Buckling Load equation looks like.

25.9461 = \frac{{3.1416}^{2} \cdot 50 \cdot 700}{{(\frac{3000}{26})}^{2}}

25.9461N = \frac{{3.1416}^{2} \cdot 50MPa \cdot 700mm²}{{(\frac{3000mm}{26mm})}^{2}}

25.9461 = \frac{{3.1416}^{2} \cdot 50 \cdot 700}{{(\frac{3000}{26})}^{2}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Civil » Category

Columns » fx Elastic Critical Buckling Load

Elastic Critical Buckling Load Solution

Follow our step by step solution on how to calculate Elastic Critical Buckling Load?

FIRST Step Consider the formula

P Buckling Load = \frac{π^{2} \cdot E \cdot A}{{(\frac{L}{r gyration})}^{2}}

Next Step Substitute values of Variables

∴

P Buckling Load = \frac{π^{2} \cdot 50MPa \cdot 700mm²}{{(\frac{3000mm}{26mm})}^{2}}

Next Step Substitute values of Constants

∴

P Buckling Load = \frac{{3.1416}^{2} \cdot 50MPa \cdot 700mm²}{{(\frac{3000mm}{26mm})}^{2}}

Next Step Prepare to Evaluate

∴

P Buckling Load = \frac{{3.1416}^{2} \cdot 50 \cdot 700}{{(\frac{3000}{26})}^{2}}

Next Step Evaluate

∴

P Buckling Load = 25.9460933477527N

LAST Step Rounding Answer

∴

P Buckling Load = 25.9461N

Elastic Critical Buckling Load Formula Elements

Variables

Constants

Buckling Load

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.

Symbol: P_{Buckling Load}

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Buckling Load

Modulus of Elasticity

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.

Symbol: E

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity

Column Cross-Sectional Area

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.

Symbol: A

Measurement: AreaUnit: mm²

Note: Value should be greater than 0.

Formulas to find Column Cross-Sectional Area

Effective Length of Column

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.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Effective Length of Column

Radius of Gyration of Column

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.

Symbol: r_gyration

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Gyration of Column

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

Other formulas in Slender Columns category

Go Cross-Sectional Area given Elastic Critical Buckling Load

A = \frac{P Buckling Load \cdot {(\frac{L}{r gyration})}^{2}}{π^{2} \cdot E}

Go Radius of Gyration of Column given Elastic Critical Buckling Load

r gyration = \sqrt{\frac{P Buckling Load \cdot L^{2}}{π^{2} \cdot E \cdot A}}

Go Slenderness Ratio given Elastic Critical Buckling Load

λ = \sqrt{\frac{π^{2} \cdot E \cdot A}{P Buckling Load}}

How to Evaluate Elastic Critical Buckling Load?

Elastic Critical Buckling Load evaluator uses Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2 to evaluate the Buckling Load, The Elastic Critical Buckling Load formula is defined as the greatest load applied on pin ended columns that cause lateral deflection i.e., failure due to buckling. Buckling Load is denoted by P_{Buckling Load} symbol.

How to evaluate Elastic Critical Buckling Load using this online evaluator? To use this online evaluator for Elastic Critical Buckling Load, enter Modulus of Elasticity (E), Column Cross-Sectional Area (A), Effective Length of Column (L) & Radius of Gyration of Column (r_gyration) and hit the calculate button.

FAQs on Elastic Critical Buckling Load

What is the formula to find Elastic Critical Buckling Load?

The formula of Elastic Critical Buckling Load is expressed as Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2. Here is an example- 2.6E+7 = (pi^2*50000000*0.0007)/(3/0.026)^2.

How to calculate Elastic Critical Buckling Load?

With Modulus of Elasticity (E), Column Cross-Sectional Area (A), Effective Length of Column (L) & Radius of Gyration of Column (r_gyration) we can find Elastic Critical Buckling Load using the formula - Buckling Load = (pi^2*Modulus of Elasticity*Column Cross-Sectional Area)/(Effective Length of Column/Radius of Gyration of Column)^2. This formula also uses Archimedes' constant .

Can the Elastic Critical Buckling Load be negative?

No, the Elastic Critical Buckling Load, measured in Force cannot be negative.

Which unit is used to measure Elastic Critical Buckling Load?

Elastic Critical Buckling Load is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Elastic Critical Buckling Load can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Elastic Critical Buckling Load Formula

Elastic Critical Buckling Load Example

Elastic Critical Buckling Load Solution

Elastic Critical Buckling Load Formula Elements

Other formulas in Slender Columns category

How to Evaluate Elastic Critical Buckling Load?

FAQs on Elastic Critical Buckling Load

Variable Name