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

✖Distance of Deflection from end A is the distance x of deflection from end A.ⓘ Distance of Deflection from end A [x]			+10% -10%
✖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 given Final Deflection at Distance X from End A of Column [l]

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

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Distance of Deflection from end A: 35 Millimeter --> 0.035 Meter (Check conversion here)
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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = (pi*x)/(asin(δ_c/((1/(1-(P/P_E)))*C))) --> (pi*0.035)/(asin(0.012/((1/(1-(3600/4000)))*0.3)))

Evaluating ... ...

l = 27.4888624147498

STEP 3: Convert Result to Output's Unit

27.4888624147498 Meter -->27488.8624147498 Millimeter (Check conversion here)

FINAL ANSWER

27488.8624147498 ≈ 27488.86 Millimeter <-- Length of Column

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Initial Curvature » Length of Column 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)

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

LaTeX Go

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

What is Euler Load?

The Euler Load (or Euler’s Critical Load) refers to the maximum axial load a slender column can bear before it buckles. It was derived by Swiss mathematician Leonhard Euler and is a key concept in structural engineering when analyzing column stability. Buckling occurs when a column under compressive load becomes unstable and deflects laterally, potentially leading to failure even if the material hasn’t reached its compressive strength limit.

How to Calculate 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 calculator 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 calculate 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 calculate Length of Column given Final Deflection at Distance X from End A of Column using this online calculator? To use this online calculator 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. Here is how the Length of Column given Final Deflection at Distance X from End A of Column calculation can be explained with given input values -> 2.7E+7 = (pi*0.035)/(asin(0.012/((1/(1-(3600/4000)))*0.3))).

FAQ

What is Length of Column given Final Deflection at Distance X from End A 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 and is represented as l = (pi*x)/(asin(δ_c/((1/(1-(P/P_E)))*C))) or Length of Column = (pi*Distance of Deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection))). Distance of Deflection from end A is the distance x of deflection from end A, 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.

How to calculate Length of Column given Final Deflection at Distance X from End A 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 is calculated using Length of Column = (pi*Distance of Deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection))). To calculate Length of Column given Final Deflection at Distance X from End A of Column, you need Distance of Deflection from end A (x), Deflection of Column (δ_c), Crippling Load (P), Euler Load (P_E) & Maximum Initial Deflection (C). With our tool, you need to enter the respective value for Distance of Deflection from end A, Deflection of Column, Crippling Load, Euler Load & Maximum Initial Deflection 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 Length of Column?

In this formula, Length of Column uses Distance of Deflection from end A, Deflection of Column, Crippling Load, Euler Load & Maximum Initial Deflection. We can use 2 other way(s) to calculate the same, which is/are as follows -

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))

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