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Value of Distance 'X' given Final Deflection at Distance X from end A of Column Formula

GoValue of Distance 'X' given Initial Deflection at Distance X from end A Formula

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

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

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

Value of Distance 'X' given Final Deflection at Distance X from end A of Column Example

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

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

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

35 = (a \sin (\frac{18.4711}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot 300})) \cdot \frac{5000}{3.1416}

35mm = (a \sin (\frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot 300mm})) \cdot \frac{5000mm}{3.1416}

35 = (a \sin (\frac{18.4711}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot 300})) \cdot \frac{5000}{3.1416}

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Value of Distance 'X' given Final Deflection at Distance X from end A of Column Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

x = (a \sin (\frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot 300mm})) \cdot \frac{5000mm}{π}

Next Step Substitute values of Constants

∴

x = (a \sin (\frac{18.4711mm}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot 300mm})) \cdot \frac{5000mm}{3.1416}

Next Step Convert Units

∴

x = (a \sin (\frac{0.0185m}{(\frac{1}{1 - (\frac{2571.429N}{4000N})}) \cdot 0.3m})) \cdot \frac{5m}{3.1416}

Next Step Prepare to Evaluate

∴

x = (a \sin (\frac{0.0185}{(\frac{1}{1 - (\frac{2571.429}{4000})}) \cdot 0.3})) \cdot \frac{5}{3.1416}

Next Step Evaluate

∴

x = 0.034999997234908m

Next Step Convert to Output's Unit

∴

x = 34.999997234908mm

LAST Step Rounding Answer

∴

x = 35mm

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

Variables

Constants

Functions

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

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)

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 Distance of Deflection from end A

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

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

Other formulas in Columns With Initial Curvature category

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}

Go Moment of Inertia given Euler Load

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

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

Value of Distance 'X' given Final Deflection at Distance X from end A of Column evaluator uses Distance of Deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection)))*Length of Column/pi to evaluate the Distance of Deflection from end A, The Value of Distance 'X' given Final Deflection at Distance X from end A of Column formula is defined as a method to determine the distance from the end of a column where the final deflection occurs, considering the initial curvature of the column and other factors that affect its deformation. Distance of Deflection from end A is denoted by x symbol.

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

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

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

The formula of Value of Distance 'X' given Final Deflection at Distance X from end A of Column is expressed as Distance of Deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection)))*Length of Column/pi. Here is an example- 22737.19 = (asin(0.01847108/((1/(1-(2571.429/4000)))*0.3)))*5/pi.

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

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

What are the other ways to Calculate Distance of Deflection from end A?

Here are the different ways to Calculate Distance of Deflection from end A-

Distance of Deflection from end A=(asin(Initial Deflection/Maximum Initial Deflection))*Length of Column/pi

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

Yes, the Value of Distance 'X' given Final Deflection at Distance X from end A of Column, measured in Length can be negative.

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

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

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Value of Distance 'X' given Final Deflection at Distance X from end A of Column Formula

​GoValue of Distance 'X' given Initial Deflection at Distance X from end A Formula

Value of Distance 'X' given Final Deflection at Distance X from end A of Column Example

Value of Distance 'X' given Final Deflection at Distance X from end A of Column Solution

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

Other Formulas to find Distance of Deflection from end A

Other formulas in Columns With Initial Curvature category

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

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

Variable Name

GoValue of Distance 'X' given Initial Deflection at Distance X from end A Formula