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Modulus of Elasticity of Column given Crippling Stress Formula

GoModulus of Elasticity given Crippling Load for any type of End Condition Formula

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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. Check FAQs

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

ε_c - Modulus of Elasticity of Column?σ_crippling - Crippling Stress?L_e - Effective Length of Column?r - Least Radius of Gyration of Column?π - Archimedes' constant?

Modulus of Elasticity of Column given Crippling Stress Example

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Here is how the Modulus of Elasticity of Column given Crippling Stress equation looks like with Values.

Here is how the Modulus of Elasticity of Column given Crippling Stress equation looks like with Units.

Here is how the Modulus of Elasticity of Column given Crippling Stress equation looks like.

5.0661 = \frac{0.02 \cdot 2500^{2}}{{3.1416}^{2} \cdot 50^{2}}

5.0661MPa = \frac{0.02MPa \cdot {2500mm}^{2}}{{3.1416}^{2} \cdot {50mm}^{2}}

5.0661 = \frac{0.02 \cdot 2500^{2}}{{3.1416}^{2} \cdot 50^{2}}

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Modulus of Elasticity of Column given Crippling Stress Solution

Follow our step by step solution on how to calculate Modulus of Elasticity of Column given Crippling Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ε c = \frac{0.02MPa \cdot {2500mm}^{2}}{π^{2} \cdot {50mm}^{2}}

Next Step Substitute values of Constants

∴

ε c = \frac{0.02MPa \cdot {2500mm}^{2}}{{3.1416}^{2} \cdot {50mm}^{2}}

Next Step Convert Units

∴

ε c = \frac{20000Pa \cdot {2.5m}^{2}}{{3.1416}^{2} \cdot {0.05m}^{2}}

Next Step Prepare to Evaluate

∴

ε c = \frac{20000 \cdot {2.5}^{2}}{{3.1416}^{2} \cdot {0.05}^{2}}

Next Step Evaluate

∴

ε c = 5066059.18211689Pa

Next Step Convert to Output's Unit

∴

ε c = 5.06605918211689MPa

LAST Step Rounding Answer

∴

ε c = 5.0661MPa

Modulus of Elasticity of Column given Crippling Stress Formula Elements

Variables

Constants

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

Crippling Stress

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.

Symbol: σ_crippling

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Crippling Stress

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

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

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 Modulus of Elasticity of Column

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

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

Other formulas in Estimation of Effective Length of Columns category

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

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

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

Modulus of Elasticity of Column given Crippling Stress evaluator uses Modulus of Elasticity of Column = (Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2) to evaluate 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 evaluate Modulus of Elasticity of Column given Crippling Stress using this online evaluator? To use this online evaluator 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.

FAQs on Modulus of Elasticity of Column given Crippling Stress

What is the formula to find Modulus of Elasticity of Column given Crippling Stress?

The formula of Modulus of Elasticity of Column given Crippling Stress is expressed as Modulus of Elasticity of Column = (Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2). Here is an example- 5.1E-6 = (20000*2.5^2)/(pi^2*0.05^2).

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

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

What are the other ways to Calculate Modulus of Elasticity of Column?

Here are the different ways to Calculate Modulus of Elasticity of Column-

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

Can the Modulus of Elasticity of Column given Crippling Stress be negative?

No, the Modulus of Elasticity of Column given Crippling Stress, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of Elasticity of Column given Crippling Stress?

Modulus of Elasticity of Column given Crippling Stress is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Modulus of Elasticity of Column given Crippling Stress can be measured.

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Modulus of Elasticity of Column given Crippling Stress Formula

​GoModulus of Elasticity given Crippling Load for any type of End Condition Formula

Modulus of Elasticity of Column given Crippling Stress Example

Modulus of Elasticity of Column given Crippling Stress Solution

Modulus of Elasticity of Column given Crippling Stress Formula Elements

Other Formulas to find Modulus of Elasticity of Column

Other formulas in Estimation of Effective Length of Columns category

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

FAQs on Modulus of Elasticity of Column given Crippling Stress

Variable Name

GoModulus of Elasticity given Crippling Load for any type of End Condition Formula