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Length of Column given Crippling Load if One End of Column is Fixed and Other is Free Formula

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Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions. Check FAQs

l = \sqrt{\frac{π^{2} \cdot E \cdot I}{4 \cdot P}}

l - Column Length?E - Modulus of Elasticity of Column?I - Moment of Inertia Column?P - Column Crippling Load?π - Archimedes' constant?

Length of Column given Crippling Load if One End of Column is Fixed and Other is Free Example

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Here is how the Length of Column given Crippling Load if One End of Column is Fixed and Other is Free equation looks like with Values.

Here is how the Length of Column given Crippling Load if One End of Column is Fixed and Other is Free equation looks like with Units.

Here is how the Length of Column given Crippling Load if One End of Column is Fixed and Other is Free equation looks like.

697.4053 = \sqrt{\frac{{3.1416}^{2} \cdot 10.56 \cdot 5600}{4 \cdot 3}}

697.4053mm = \sqrt{\frac{{3.1416}^{2} \cdot 10.56MPa \cdot 5600cm⁴}{4 \cdot 3kN}}

697.4053 = \sqrt{\frac{{3.1416}^{2} \cdot 10.56 \cdot 5600}{4 \cdot 3}}

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Length of Column given Crippling Load if One End of Column is Fixed and Other is Free Solution

Follow our step by step solution on how to calculate Length of Column given Crippling Load if One End of Column is Fixed and Other is Free?

FIRST Step Consider the formula

l = \sqrt{\frac{π^{2} \cdot E \cdot I}{4 \cdot P}}

Next Step Substitute values of Variables

∴

l = \sqrt{\frac{π^{2} \cdot 10.56MPa \cdot 5600cm⁴}{4 \cdot 3kN}}

Next Step Substitute values of Constants

∴

l = \sqrt{\frac{{3.1416}^{2} \cdot 10.56MPa \cdot 5600cm⁴}{4 \cdot 3kN}}

Next Step Convert Units

∴

l = \sqrt{\frac{{3.1416}^{2} \cdot 1.1E+7Pa \cdot 5.6E-5m⁴}{4 \cdot 3000N}}

Next Step Prepare to Evaluate

∴

l = \sqrt{\frac{{3.1416}^{2} \cdot 1.1E+7 \cdot 5.6E-5}{4 \cdot 3000}}

Next Step Evaluate

∴

l = 0.697405265886116m

Next Step Convert to Output's Unit

∴

l = 697.405265886116mm

LAST Step Rounding Answer

∴

l = 697.4053mm

Length of Column given Crippling Load if One End of Column is Fixed and Other is Free Formula Elements

Variables

Constants

Functions

Column Length

Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Column Length

Modulus of Elasticity of Column

Modulus of Elasticity of Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity 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

Column Crippling Load

Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Symbol: P

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Column Crippling Load

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in One End of Column is Fixed and Other is Free category

Go Moment of Section due to Crippling Load if One End of Column is Fixed and Other is Free

M t = P \cdot (a - δ)

Go Crippling Load given Moment of Section if One End of Column is Fixed and Other is Free

P = \frac{M t}{a - δ}

Go Deflection at Free End given Moment of Section if One End of Column is Fixed and Other is Free

a = \frac{M t}{P} + δ

Go Deflection of Section given Moment of Section if One End of Column is Fixed and Other is Free

δ = a - \frac{M t}{P}

How to Evaluate Length of Column given Crippling Load if One End of Column is Fixed and Other is Free?

Length of Column given Crippling Load if One End of Column is Fixed and Other is Free evaluator uses Column Length = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(4*Column Crippling Load)) to evaluate the Column Length, Length of Column given Crippling Load if One End of Column is Fixed and Other is Free formula is defined as the maximum length of a column that can withstand a crippling load when one end is fixed and the other end is free, providing a critical value for structural integrity in engineering design. Column Length is denoted by l symbol.

How to evaluate Length of Column given Crippling Load if One End of Column is Fixed and Other is Free using this online evaluator? To use this online evaluator for Length of Column given Crippling Load if One End of Column is Fixed and Other is Free, enter Modulus of Elasticity of Column (E), Moment of Inertia Column (I) & Column Crippling Load (P) and hit the calculate button.

FAQs on Length of Column given Crippling Load if One End of Column is Fixed and Other is Free

What is the formula to find Length of Column given Crippling Load if One End of Column is Fixed and Other is Free?

The formula of Length of Column given Crippling Load if One End of Column is Fixed and Other is Free is expressed as Column Length = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(4*Column Crippling Load)). Here is an example- 697405.3 = sqrt((pi^2*10560000*5.6E-05)/(4*3000)).

How to calculate Length of Column given Crippling Load if One End of Column is Fixed and Other is Free?

With Modulus of Elasticity of Column (E), Moment of Inertia Column (I) & Column Crippling Load (P) we can find Length of Column given Crippling Load if One End of Column is Fixed and Other is Free using the formula - Column Length = sqrt((pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(4*Column Crippling Load)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Length of Column given Crippling Load if One End of Column is Fixed and Other is Free be negative?

No, the Length of Column given Crippling Load if One End of Column is Fixed and Other is Free, measured in Length cannot be negative.

Which unit is used to measure Length of Column given Crippling Load if One End of Column is Fixed and Other is Free?

Length of Column given Crippling Load if One End of Column is Fixed and Other is Free is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Length of Column given Crippling Load if One End of Column is Fixed and Other is Free can be measured.

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Length of Column given Crippling Load if One End of Column is Fixed and Other is Free Formula

Length of Column given Crippling Load if One End of Column is Fixed and Other is Free Example

Length of Column given Crippling Load if One End of Column is Fixed and Other is Free Solution

Length of Column given Crippling Load if One End of Column is Fixed and Other is Free Formula Elements

Other formulas in One End of Column is Fixed and Other is Free category

How to Evaluate Length of Column given Crippling Load if One End of Column is Fixed and Other is Free?

FAQs on Length of Column given Crippling Load if One End of Column is Fixed and Other is Free

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