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Length of Column given Final Deflection at Distance X from End A of Column Formula

GoLength of Column given Initial Deflection at Distance X from end A Formula

GoLength of Column given Euler Load Formula

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Length of Column 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 = \frac{π \cdot x}{a \sin (\frac{δ c}{(\frac{1}{1 - (\frac{P}{P E})}) \cdot C})}

l - Length of Column?x - Distance of Deflection from end A?δ_c - Deflection of Column?P - Crippling Load?P_E - Euler Load?C - Maximum Initial Deflection?π - Archimedes' constant?

Length of Column given Final Deflection at Distance X from End A of Column Example

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Here is how the Length of Column given Final Deflection at Distance X from End A of Column equation looks like with Values.

Here is how the Length of Column given Final Deflection at Distance X from End A of Column equation looks like with Units.

Here is how the Length of Column given Final Deflection at Distance X from End A of Column equation looks like.

5000.0004 = \frac{3.1416 \cdot 35}{a \sin (\frac{18.4711}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot 300})}

5000.0004mm = \frac{3.1416 \cdot 35mm}{a \sin (\frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot 300mm})}

5000.0004 = \frac{3.1416 \cdot 35}{a \sin (\frac{18.4711}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot 300})}

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Length of Column given Final Deflection at Distance X from End A of Column Solution

Follow our step by step solution on how to calculate Length of Column given Final Deflection at Distance X from End A of Column?

FIRST Step Consider the formula

l = \frac{π \cdot x}{a \sin (\frac{δ c}{(\frac{1}{1 - (\frac{P}{P E})}) \cdot C})}

Next Step Substitute values of Variables

∴

l = \frac{π \cdot 35mm}{a \sin (\frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot 300mm})}

Next Step Substitute values of Constants

∴

l = \frac{3.1416 \cdot 35mm}{a \sin (\frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot 300mm})}

Next Step Convert Units

∴

l = \frac{3.1416 \cdot 0.035m}{a \sin (\frac{0.0185m}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot 0.3m})}

Next Step Prepare to Evaluate

∴

l = \frac{3.1416 \cdot 0.035}{a \sin (\frac{0.0185}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot 0.3})}

Next Step Evaluate

∴

l = 5.00000039501317m

Next Step Convert to Output's Unit

∴

l = 5000.00039501317mm

LAST Step Rounding Answer

∴

l = 5000.0004mm

Length of Column given Final Deflection at Distance X from End A of Column Formula Elements

Variables

Constants

Functions

Length of Column

Length of Column 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 Length of Column

Distance of Deflection from end A

Distance of Deflection from end A is the distance x of deflection from end A.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance of Deflection from end A

Deflection of Column

Deflection of Column is the displacement or bending of a column from its original, vertical position when subjected to an external load, particularly a compressive load.

Symbol: δ_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Column

Crippling Load

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

Symbol: P

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Crippling Load

Euler Load

Euler load is the compressive load at which a slender column will suddenly bend or buckle.

Symbol: P_E

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Euler Load

Maximum Initial Deflection

Maximum Initial Deflection is the degree to which a structural element is displaced under a load.

Symbol: C

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Maximum Initial Deflection

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

asin

The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: asin(Number)

Other Formulas to find Length of Column

Go Length of Column given Initial Deflection at Distance X from end A

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

Go Length of Column given Euler Load

l = \sqrt{\frac{(π^{2}) \cdot ε column \cdot I}{P E}}

Other formulas in Columns With Initial Curvature category

Go Value of Distance 'X' given Initial Deflection at Distance X from end A

x = (a \sin (\frac{y'}{C})) \cdot \frac{l}{π}

Go Euler Load

P E = \frac{(π^{2}) \cdot ε column \cdot I}{l^{2}}

Go Modulus of Elasticity given Euler Load

ε column = \frac{P E \cdot (l^{2})}{π^{2} \cdot I}

Go Moment of Inertia given Euler Load

I = \frac{P E \cdot (l^{2})}{(π^{2}) \cdot ε column}

How to Evaluate Length of Column given Final Deflection at Distance X from End A of Column?

Length of Column given Final Deflection at Distance X from End A of Column evaluator uses Length of Column = (pi*Distance of Deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection))) to evaluate the Length of Column, The Length of Column given Final Deflection at Distance X from End A of Column formula is defined as a measure of the length of a column with initial curvature, considering the final deflection at a specific distance from the end of the column, providing valuable insights into the column's structural behavior. Length of Column is denoted by l symbol.

How to evaluate Length of Column given Final Deflection at Distance X from End A of Column using this online evaluator? To use this online evaluator for Length of Column given Final Deflection at Distance X from End A of Column, enter Distance of Deflection from end A (x), Deflection of Column (δ_c), Crippling Load (P), Euler Load (P_E) & Maximum Initial Deflection (C) and hit the calculate button.

FAQs on Length of Column given Final Deflection at Distance X from End A of Column

What is the formula to find Length of Column given Final Deflection at Distance X from End A of Column?

The formula of Length of Column given Final Deflection at Distance X from End A of Column is expressed as Length of Column = (pi*Distance of Deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection))). Here is an example- 7.7E+6 = (pi*0.035)/(asin(0.01847108/((1/(1-(2571.429/4000)))*0.3))).

How to calculate Length of Column given Final Deflection at Distance X from End A of Column?

With Distance of Deflection from end A (x), Deflection of Column (δ_c), Crippling Load (P), Euler Load (P_E) & Maximum Initial Deflection (C) we can find Length of Column given Final Deflection at Distance X from End A of Column using the formula - Length of Column = (pi*Distance of Deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection))). This formula also uses Archimedes' constant and , Sine (sin), Inverse Sine (asin) function(s).

What are the other ways to Calculate Length of Column?

Here are the different ways to Calculate Length of Column-

Length of Column=(pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection))
Length of Column=sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load))

Can the Length of Column given Final Deflection at Distance X from End A of Column be negative?

No, the Length of Column given Final Deflection at Distance X from End A of Column, measured in Length cannot be negative.

Which unit is used to measure Length of Column given Final Deflection at Distance X from End A of Column?

Length of Column given Final Deflection at Distance X from End A of Column 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 Final Deflection at Distance X from End A of Column can be measured.

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Length of Column given Final Deflection at Distance X from End A of Column Formula

​GoLength of Column given Initial Deflection at Distance X from end A Formula

​GoLength of Column given Euler Load Formula

Length of Column given Final Deflection at Distance X from End A of Column Example

Length of Column given Final Deflection at Distance X from End A of Column Solution

Length of Column given Final Deflection at Distance X from End A of Column Formula Elements

Other Formulas to find Length of Column

Other formulas in Columns With Initial Curvature category

How to Evaluate Length of Column given Final Deflection at Distance X from End A of Column?

FAQs on Length of Column given Final Deflection at Distance X from End A of Column

Variable Name

GoLength of Column given Initial Deflection at Distance X from end A Formula

GoLength of Column given Euler Load Formula