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

GoModulus of Elasticity of Column given Crippling Stress 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{P cr \cdot {L e}^{2}}{π^{2} \cdot I}

ε_c - Modulus of Elasticity of Column?P_cr - Column Crippling Load?L_e - Effective Length of Column?I - Moment of Inertia Column?π - Archimedes' constant?

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

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Here is how the Modulus of Elasticity given Crippling Load for any type of End Condition equation looks like with Values.

Here is how the Modulus of Elasticity given Crippling Load for any type of End Condition equation looks like with Units.

Here is how the Modulus of Elasticity given Crippling Load for any type of End Condition equation looks like.

10.5543 = \frac{10000 \cdot 2500^{2}}{{3.1416}^{2} \cdot 60000}

10.5543MPa = \frac{10000N \cdot {2500mm}^{2}}{{3.1416}^{2} \cdot 60000cm⁴}

10.5543 = \frac{10000 \cdot 2500^{2}}{{3.1416}^{2} \cdot 60000}

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

Follow our step by step solution on how to calculate Modulus of Elasticity given Crippling Load for any type of End Condition?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ε c = \frac{10000N \cdot {2500mm}^{2}}{π^{2} \cdot 60000cm⁴}

Next Step Substitute values of Constants

∴

ε c = \frac{10000N \cdot {2500mm}^{2}}{{3.1416}^{2} \cdot 60000cm⁴}

Next Step Convert Units

∴

ε c = \frac{10000N \cdot {2.5m}^{2}}{{3.1416}^{2} \cdot 0.0006m⁴}

Next Step Prepare to Evaluate

∴

ε c = \frac{10000 \cdot {2.5}^{2}}{{3.1416}^{2} \cdot 0.0006}

Next Step Evaluate

∴

ε c = 10554289.9627435Pa

Next Step Convert to Output's Unit

∴

ε c = 10.5542899627435MPa

LAST Step Rounding Answer

∴

ε c = 10.5543MPa

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

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

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

Moment of Inertia Column

Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.

Symbol: I

Measurement: Second Moment of AreaUnit: cm⁴

Note: Value should be greater than 0.

Formulas to find Moment of Inertia 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 of Column given Crippling Stress

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

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 given Crippling Load for any type of End Condition?

Modulus of Elasticity given Crippling Load for any type of End Condition evaluator uses Modulus of Elasticity of Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Moment of Inertia Column) to evaluate the Modulus of Elasticity of Column, Modulus of Elasticity given Crippling Load for any type of End Condition formula is defined as a measure of the stiffness of a material, which is the ratio of stress to strain within the proportional limit of the material, and is used to determine the crippling load of a column under various end conditions. Modulus of Elasticity of Column is denoted by ε_c symbol.

How to evaluate Modulus of Elasticity given Crippling Load for any type of End Condition using this online evaluator? To use this online evaluator for Modulus of Elasticity given Crippling Load for any type of End Condition, enter Column Crippling Load (P_cr), Effective Length of Column (L_e) & Moment of Inertia Column (I) and hit the calculate button.

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

What is the formula to find Modulus of Elasticity given Crippling Load for any type of End Condition?

The formula of Modulus of Elasticity given Crippling Load for any type of End Condition is expressed as Modulus of Elasticity of Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Moment of Inertia Column). Here is an example- 1.1E-5 = (10000*2.5^2)/(pi^2*0.0006).

How to calculate Modulus of Elasticity given Crippling Load for any type of End Condition?

With Column Crippling Load (P_cr), Effective Length of Column (L_e) & Moment of Inertia Column (I) we can find Modulus of Elasticity given Crippling Load for any type of End Condition using the formula - Modulus of Elasticity of Column = (Column Crippling Load*Effective Length of Column^2)/(pi^2*Moment of Inertia Column). 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=(Crippling Stress*Effective Length of Column^2)/(pi^2*Least Radius of Gyration of Column^2)

Can the Modulus of Elasticity given Crippling Load for any type of End Condition be negative?

No, the Modulus of Elasticity given Crippling Load for any type of End Condition, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of Elasticity given Crippling Load for any type of End Condition?

Modulus of Elasticity given Crippling Load for any type of End Condition 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 given Crippling Load for any type of End Condition can be measured.

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

​GoModulus of Elasticity of Column given Crippling Stress Formula

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

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

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

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

Variable Name

GoModulus of Elasticity of Column given Crippling Stress Formula