FormulaDen.com

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

Crippling Load given Effective Length and Radius of Gyration Formula

GoCrippling Load for any type of End Condition Formula

Fx Copy

LaTeX Copy

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. Check FAQs

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

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

Crippling Load given Effective Length and Radius of Gyration Example

With values

With units

Only example

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

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

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

260557.5562 = \frac{{3.1416}^{2} \cdot 10.56 \cdot 6.25 \cdot 50^{2}}{2500^{2}}

260557.5562N = \frac{{3.1416}^{2} \cdot 10.56MPa \cdot 6.25m² \cdot {50mm}^{2}}{{2500mm}^{2}}

260557.5562 = \frac{{3.1416}^{2} \cdot 10.56 \cdot 6.25 \cdot 50^{2}}{2500^{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

Structural Engineering » fx Crippling Load given Effective Length and Radius of Gyration

Crippling Load given Effective Length and Radius of Gyration Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

P cr = \frac{π^{2} \cdot 10.56MPa \cdot 6.25m² \cdot {50mm}^{2}}{{2500mm}^{2}}

Next Step Substitute values of Constants

∴

P cr = \frac{{3.1416}^{2} \cdot 10.56MPa \cdot 6.25m² \cdot {50mm}^{2}}{{2500mm}^{2}}

Next Step Convert Units

∴

P cr = \frac{{3.1416}^{2} \cdot 1.1E+7Pa \cdot 6.25m² \cdot {0.05m}^{2}}{{2.5m}^{2}}

Next Step Prepare to Evaluate

∴

P cr = \frac{{3.1416}^{2} \cdot 1.1E+7 \cdot 6.25 \cdot {0.05}^{2}}{{2.5}^{2}}

Next Step Evaluate

∴

P cr = 260557.556188759N

LAST Step Rounding Answer

∴

P cr = 260557.5562N

Crippling Load given Effective Length and Radius of Gyration Formula Elements

Variables

Constants

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

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

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

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

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 to find Column Crippling Load

Go Crippling Load for any type of End Condition

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

Other formulas in Crippling Load category

Go Crippling Stress

σ crippling = \frac{π^{2} \cdot ε c \cdot r^{2}}{{L e}^{2}}

Go Crippling Stress given Crippling Load

σ crippling = \frac{P cr}{A}

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

Crippling Load given Effective Length and Radius of Gyration evaluator uses Column Crippling Load = (pi^2*Modulus of Elasticity of Column*Column Cross-Sectional Area*Least Radius of Gyration of Column^2)/(Effective Length of Column^2) to evaluate the Column Crippling Load, Crippling Load given Effective Length and Radius of Gyration formula is defined as the maximum load that a column can withstand without buckling or collapsing, taking into account the effective length of the column and its radius of gyration, which are critical factors in determining the column's stability and strength. Column Crippling Load is denoted by P_cr symbol.

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

FAQs on Crippling Load given Effective Length and Radius of Gyration

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

The formula of Crippling Load given Effective Length and Radius of Gyration is expressed as Column Crippling Load = (pi^2*Modulus of Elasticity of Column*Column Cross-Sectional Area*Least Radius of Gyration of Column^2)/(Effective Length of Column^2). Here is an example- 260557.6 = (pi^2*10560000*6.25*0.05^2)/(2.5^2).

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

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

What are the other ways to Calculate Column Crippling Load?

Here are the different ways to Calculate Column Crippling Load-

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

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

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

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

Crippling Load given Effective Length and Radius of Gyration is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Crippling Load given Effective Length and Radius of Gyration can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

Crippling Load given Effective Length and Radius of Gyration Formula

​GoCrippling Load for any type of End Condition Formula

Crippling Load given Effective Length and Radius of Gyration Example

Crippling Load given Effective Length and Radius of Gyration Solution

Crippling Load given Effective Length and Radius of Gyration Formula Elements

Other Formulas to find Column Crippling Load

Other formulas in Crippling Load category

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

FAQs on Crippling Load given Effective Length and Radius of Gyration

Variable Name

GoCrippling Load for any type of End Condition Formula