Modulus of Elasticity of Column given Crippling Stress Calculator

✖Crippling stress refers to the stress level at which a structural element, such as a column, experiences local instability or failure due to buckling, particularly relevant for thin-walled columns.ⓘ Crippling Stress [σ_crippling]			+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%
✖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%

✖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 given Crippling Stress [ε_c]

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Modulus of Elasticity of Column given Crippling Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of Elasticity of Column = (Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2)
ε_c = (σ_crippling*L_e^2)/(pi^2*r^2)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Crippling Stress - (Measured in Pascal) - Crippling stress refers to the stress level at which a structural element, such as a column, experiences local instability or failure due to buckling, particularly relevant for thin-walled columns.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Crippling Stress: 0.02 Megapascal --> 20000 Pascal (Check conversion here)
Effective Length of Column: 2500 Millimeter --> 2.5 Meter (Check conversion here)
Least Radius of Gyration of Column: 50 Millimeter --> 0.05 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_c = (σ_crippling*L_e^2)/(pi^2*r^2) --> (20000*2.5^2)/(pi^2*0.05^2)

Evaluating ... ...

ε_c = 5066059.18211689

STEP 3: Convert Result to Output's Unit

5066059.18211689 Pascal -->5.06605918211689 Megapascal (Check conversion here)

FINAL ANSWER

5.06605918211689 ≈ 5.066059 Megapascal <-- Modulus of Elasticity of Column

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< Estimation of Effective Length of Columns Calculators

Actual Length given Slenderness Ratio

LaTeX Go Length of Column = Slenderness Ratio*Least Radius of Gyration of Column

Actual Length of Column given Effective Length if One End is Fixed Other is Hinged

LaTeX Go Length of Column = sqrt(2)*Effective Length of Column

Actual Length of Column given Effective Length if One End is Fixed Other is Free

LaTeX Go Length of Column = Effective Length of Column/2

Actual Length of Column given Effective Length if Both Ends of Column are Fixed

LaTeX Go Length of Column = 2*Effective Length of Column

< Modulus of elasticity Calculators

Modulus of Elasticity of Column given Crippling Stress

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

Modulus of Elasticity given Crippling Load for any type of End Condition

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

Moment of Inertia given Crippling Load for any type of End Condition

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

Modulus of Elasticity of Column given Crippling Stress Formula

LaTeX Go

Modulus of Elasticity of Column = (Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2)
ε_c = (σ_crippling*L_e^2)/(pi^2*r^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 Modulus of Elasticity of Column given Crippling Stress?

Modulus of Elasticity of Column given Crippling Stress calculator uses Modulus of Elasticity of Column = (Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2) to calculate the Modulus of Elasticity of Column, Modulus of Elasticity of Column given Crippling Stress formula is defined as a measure of the ability of a column to resist deformation under axial compressive load, providing a critical value of stress at which the column will buckle or cripple, which is essential in designing stable column structures. Modulus of Elasticity of Column is denoted by ε_c symbol.

How to calculate Modulus of Elasticity of Column given Crippling Stress using this online calculator? To use this online calculator for Modulus of Elasticity of Column given Crippling Stress, enter Crippling Stress (σ_crippling), Effective Length of Column (L_e) & Least Radius of Gyration of Column (r) and hit the calculate button. Here is how the Modulus of Elasticity of Column given Crippling Stress calculation can be explained with given input values -> 5.1E-6 = (20000*2.5^2)/(pi^2*0.05^2).

FAQ

What is Modulus of Elasticity of Column given Crippling Stress?

Modulus of Elasticity of Column given Crippling Stress formula is defined as a measure of the ability of a column to resist deformation under axial compressive load, providing a critical value of stress at which the column will buckle or cripple, which is essential in designing stable column structures and is represented as ε_c = (σ_crippling*L_e^2)/(pi^2*r^2) or Modulus of Elasticity of Column = (Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2). Crippling stress refers to the stress level at which a structural element, such as a column, experiences local instability or failure due to buckling, particularly relevant for thin-walled columns, 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 & 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.

How to calculate Modulus of Elasticity of Column given Crippling Stress?

Modulus of Elasticity of Column given Crippling Stress formula is defined as a measure of the ability of a column to resist deformation under axial compressive load, providing a critical value of stress at which the column will buckle or cripple, which is essential in designing stable column structures is calculated using Modulus of Elasticity of Column = (Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2). To calculate Modulus of Elasticity of Column given Crippling Stress, you need Crippling Stress (σ_crippling), Effective Length of Column (L_e) & Least Radius of Gyration of Column (r). With our tool, you need to enter the respective value for Crippling Stress, Effective Length of Column & Least Radius of Gyration 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 Modulus of Elasticity of Column?

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

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

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