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Final Deflection at Distance X from end A of Column Formula

GoMaximum Deflection for Columns with Initial Curvature Formula

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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. Check FAQs

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

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

Final Deflection at Distance X from end A of Column Example

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

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

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

65.9681 = (\frac{1}{1 - (\frac{3.6}{4})}) \cdot 300 \cdot \sin (\frac{3.1416 \cdot 35}{5000})

65.9681mm = (\frac{1}{1 - (\frac{3.6kN}{4kN})}) \cdot 300mm \cdot \sin (\frac{3.1416 \cdot 35mm}{5000mm})

65.9681 = (\frac{1}{1 - (\frac{3.6}{4})}) \cdot 300 \cdot \sin (\frac{3.1416 \cdot 35}{5000})

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Final Deflection at Distance X from end A of Column Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ c = (\frac{1}{1 - (\frac{3.6kN}{4kN})}) \cdot 300mm \cdot \sin (\frac{π \cdot 35mm}{5000mm})

Next Step Substitute values of Constants

∴

δ c = (\frac{1}{1 - (\frac{3.6kN}{4kN})}) \cdot 300mm \cdot \sin (\frac{3.1416 \cdot 35mm}{5000mm})

Next Step Convert Units

∴

δ c = (\frac{1}{1 - (\frac{3600N}{4000N})}) \cdot 0.3m \cdot \sin (\frac{3.1416 \cdot 0.035m}{5m})

Next Step Prepare to Evaluate

∴

δ c = (\frac{1}{1 - (\frac{3600}{4000})}) \cdot 0.3 \cdot \sin (\frac{3.1416 \cdot 0.035}{5})

Next Step Evaluate

∴

δ c = 0.0659681282775153m

Next Step Convert to Output's Unit

∴

δ c = 65.9681282775153mm

LAST Step Rounding Answer

∴

δ c = 65.9681mm

Final Deflection at Distance X from end A of Column Formula Elements

Variables

Constants

Functions

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: kN

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: kN

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

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

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

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)

Other Formulas to find Deflection of Column

Go Maximum Deflection for Columns with Initial Curvature

δ c = (\frac{1}{1 - (\frac{P}{P E})}) \cdot C

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

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

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}

How to Evaluate Final Deflection at Distance X from end A of Column?

Final Deflection at Distance X from end A of Column evaluator uses Deflection of Column = (1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column) to evaluate the Deflection of Column, The Final Deflection at Distance X from end A of Column formula is defined as a measure of the deflection at a specific point from the end of a column, taking into account the initial curvature of the column, which is essential in structural analysis and design to ensure stability and safety. Deflection of Column is denoted by δ_c symbol.

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

FAQs on Final Deflection at Distance X from end A of Column

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

The formula of Final Deflection at Distance X from end A of Column is expressed as Deflection of Column = (1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column). Here is an example- 65968.13 = (1/(1-(3600/4000)))*0.3*sin((pi*0.035)/5).

How to calculate Final Deflection at Distance X from end A of Column?

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

What are the other ways to Calculate Deflection of Column?

Here are the different ways to Calculate Deflection of Column-

Deflection of Column=(1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection

Can the Final Deflection at Distance X from end A of Column be negative?

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

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

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 Final Deflection at Distance X from end A of Column can be measured.

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Final Deflection at Distance X from end A of Column Formula

​GoMaximum Deflection for Columns with Initial Curvature Formula

Final Deflection at Distance X from end A of Column Example

Final Deflection at Distance X from end A of Column Solution

Final Deflection at Distance X from end A of Column Formula Elements

Other Formulas to find Deflection of Column

Other formulas in Columns With Initial Curvature category

How to Evaluate Final Deflection at Distance X from end A of Column?

FAQs on Final Deflection at Distance X from end A of Column

Variable Name

GoMaximum Deflection for Columns with Initial Curvature Formula