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

✖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.ⓘ Deflection of Column [δ_c]			+10% -10%
✖Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.ⓘ Crippling Load [P]			+10% -10%
✖Euler load is the compressive load at which a slender column will suddenly bend or buckle.ⓘ Euler Load [P_E]			+10% -10%
✖Maximum Initial Deflection is the degree to which a structural element is displaced under a load.ⓘ Maximum Initial Deflection [C]			+10% -10%
✖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.ⓘ Length of Column [l]			+10% -10%

✖Distance of Deflection from end A is the distance x of deflection from end A.ⓘ Value of Distance 'X' given Final Deflection at Distance X from end A of Column [x]

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

STEP 0: Pre-Calculation Summary

Formula Used

Distance of Deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection)))*Length of Column/pi
x = (asin(δ_c/((1/(1-(P/P_E)))*C)))*l/pi
This formula uses 1 Constants, 2 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., 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., asin(Number)

Variables Used

Distance of Deflection from end A - (Measured in Meter) - Distance of Deflection from end A is the distance x of deflection from end A.
Deflection of Column - (Measured in Meter) - 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.
Crippling Load - (Measured in Newton) - Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.
Euler Load - (Measured in Newton) - Euler load is the compressive load at which a slender column will suddenly bend or buckle.
Maximum Initial Deflection - (Measured in Meter) - Maximum Initial Deflection is the degree to which a structural element is displaced under a load.
Length of Column - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Deflection of Column: 12 Millimeter --> 0.012 Meter (Check conversion here)
Crippling Load: 3600 Newton --> 3600 Newton No Conversion Required
Euler Load: 4000 Newton --> 4000 Newton No Conversion Required
Maximum Initial Deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)
Length of Column: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = (asin(δ_c/((1/(1-(P/P_E)))*C)))*l/pi --> (asin(0.012/((1/(1-(3600/4000)))*0.3)))*5/pi

Evaluating ... ...

x = 0.00636621470032531

STEP 3: Convert Result to Output's Unit

0.00636621470032531 Meter -->6.36621470032531 Millimeter (Check conversion here)

FINAL ANSWER

6.36621470032531 ≈ 6.366215 Millimeter <-- Distance of Deflection from end A

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Initial Curvature » Value of Distance 'X' given Final Deflection at Distance X from end A of Column

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Columns With Initial Curvature Calculators

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

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

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

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

Modulus of Elasticity given Euler Load

LaTeX Go Modulus of Elasticity of Column = (Euler Load*(Length of Column^2))/(pi^2*Moment of Inertia)

Euler Load

LaTeX Go Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)

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

LaTeX Go

Distance of Deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection)))*Length of Column/pi
x = (asin(δ_c/((1/(1-(P/P_E)))*C)))*l/pi

What is Buckling or Crippling Load?

Buckling Load is the highest load at which the column will buckle. Crippling load is the max load beyond that load, it cant use further it becomes disable to use.

How to Calculate 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 calculator 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 calculate 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 calculate Value of Distance 'X' given Final Deflection at Distance X from end A of Column using this online calculator? To use this online calculator 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. Here is how the Value of Distance 'X' given Final Deflection at Distance X from end A of Column calculation can be explained with given input values -> 6366.215 = (asin(0.012/((1/(1-(3600/4000)))*0.3)))*5/pi.

FAQ

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

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 and is represented as x = (asin(δ_c/((1/(1-(P/P_E)))*C)))*l/pi or Distance of Deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection)))*Length of Column/pi. 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, Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself, Euler load is the compressive load at which a slender column will suddenly bend or buckle, Maximum Initial Deflection is the degree to which a structural element is displaced under a load & 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.

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

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 is calculated using Distance of Deflection from end A = (asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection)))*Length of Column/pi. To calculate Value of Distance 'X' given Final Deflection at Distance X from end A of Column, you need Deflection of Column (δ_c), Crippling Load (P), Euler Load (P_E), Maximum Initial Deflection (C) & Length of Column (l). With our tool, you need to enter the respective value for Deflection of Column, Crippling Load, Euler Load, Maximum Initial Deflection & Length of Column and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Distance of Deflection from end A?

In this formula, Distance of Deflection from end A uses Deflection of Column, Crippling Load, Euler Load, Maximum Initial Deflection & Length of Column. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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