Crippling Load given Effective Length and Radius of Gyration Calculator

✖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.ⓘ Least Radius of Gyration of Column [r]			+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%

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

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Crippling Load given Effective Length and Radius of Gyration Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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
Least Radius of Gyration of Column: 50 Millimeter --> 0.05 Meter (Check conversion here)
Effective Length of Column: 2500 Millimeter --> 2.5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_cr = (pi^2*ε_c*A*r^2)/(L_e^2) --> (pi^2*10560000*6.25*0.05^2)/(2.5^2)

Evaluating ... ...

P_cr = 260557.556188759

STEP 3: Convert Result to Output's Unit

260557.556188759 Newton --> No Conversion Required

FINAL ANSWER

260557.556188759 ≈ 260557.6 Newton <-- Column Crippling Load

(Calculation completed in 00.004 seconds)

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< Crippling Load Calculators

Crippling Load given Effective Length and Radius of Gyration

LaTeX Go 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)

Crippling Stress

LaTeX Go Crippling Stress = (pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/(Effective Length of Column^2)

Crippling Load for any type of End Condition

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

Crippling Stress given Crippling Load

LaTeX Go Crippling Stress = Column Crippling Load/Column Cross-Sectional Area

< Crippling Load and Stress Calculators

Crippling Load given Effective Length and Radius of Gyration

LaTeX Go 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)

Crippling Stress

LaTeX Go Crippling Stress = (pi^2*Modulus of Elasticity of Column*Least Radius of Gyration of Column^2)/(Effective Length of Column^2)

Crippling Load for any type of End Condition

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

Crippling Stress given Crippling Load

LaTeX Go Crippling Stress = Column Crippling Load/Column Cross-Sectional Area

Crippling Load given Effective Length and Radius of Gyration Formula

LaTeX Go

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)
P_cr = (pi^2*ε_c*A*r^2)/(L_e^2)

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 Crippling Load given Effective Length and Radius of Gyration?

Crippling Load given Effective Length and Radius of Gyration calculator 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 calculate 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 calculate Crippling Load given Effective Length and Radius of Gyration using this online calculator? To use this online calculator 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. Here is how the Crippling Load given Effective Length and Radius of Gyration calculation can be explained with given input values -> 260557.6 = (pi^2*10560000*6.25*0.05^2)/(2.5^2).

FAQ

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

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

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

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 is calculated using 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 calculate Crippling Load given Effective Length and Radius of Gyration, you need 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). With our tool, you need to enter the respective value for Modulus of Elasticity of Column, Column Cross-Sectional Area, Least Radius of Gyration of Column & Effective Length of Column 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 Column Crippling Load?

In this formula, Column Crippling Load uses Modulus of Elasticity of Column, Column Cross-Sectional Area, Least Radius of Gyration of Column & Effective Length of Column. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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