Length of Column given Initial Deflection at Distance X from end A 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%
✖Initial Deflection is the deformation that a structural component experiences before any external load is applied or due to inherent imperfections such as residual stresses etc.ⓘ Initial Deflection [y']			+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 Initial Deflection at Distance X from end A [l]

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

STEP 0: Pre-Calculation Summary

Formula Used

Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection))
l = (pi*x)/(asin(y'/C))
This formula uses 1 Constants, 2 Functions, 4 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.
Initial Deflection - (Measured in Meter) - Initial Deflection is the deformation that a structural component experiences before any external load is applied or due to inherent imperfections such as residual stresses etc.
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)
Initial Deflection: 60 Millimeter --> 0.06 Meter (Check conversion here)
Maximum Initial Deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = (pi*x)/(asin(y'/C)) --> (pi*0.035)/(asin(0.06/0.3))

Evaluating ... ...

l = 0.54607110782663

STEP 3: Convert Result to Output's Unit

0.54607110782663 Meter -->546.07110782663 Millimeter (Check conversion here)

FINAL ANSWER

546.07110782663 ≈ 546.0711 Millimeter <-- Length of Column

(Calculation completed in 00.008 seconds)

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

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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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 Initial Deflection at Distance X from end A Formula

LaTeX Go

Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection))
l = (pi*x)/(asin(y'/C))

What is Deflection?

Deflection refers to the displacement or deformation of a structural element, such as a beam, column, or cantilever, under an applied load. It is the distance by which a point on the element moves from its original, unloaded position due to the forces or moments acting on it.

How to Calculate Length of Column given Initial Deflection at Distance X from end A?

Length of Column given Initial Deflection at Distance X from end A calculator uses Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection)) to calculate the Length of Column, The Length of Column given Initial Deflection at Distance X from end A formula is defined as a calculation that determines the length of a column with initial curvature, taking into account the initial deflection at a specific distance from end A, providing a crucial parameter in structural analysis and design. Length of Column is denoted by l symbol.

How to calculate Length of Column given Initial Deflection at Distance X from end A using this online calculator? To use this online calculator for Length of Column given Initial Deflection at Distance X from end A, enter Distance of Deflection from end A (x), Initial Deflection (y') & Maximum Initial Deflection (C) and hit the calculate button. Here is how the Length of Column given Initial Deflection at Distance X from end A calculation can be explained with given input values -> 546071.1 = (pi*0.035)/(asin(0.06/0.3)).

FAQ

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

The Length of Column given Initial Deflection at Distance X from end A formula is defined as a calculation that determines the length of a column with initial curvature, taking into account the initial deflection at a specific distance from end A, providing a crucial parameter in structural analysis and design and is represented as l = (pi*x)/(asin(y'/C)) or Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection)). Distance of Deflection from end A is the distance x of deflection from end A, Initial Deflection is the deformation that a structural component experiences before any external load is applied or due to inherent imperfections such as residual stresses etc & Maximum Initial Deflection is the degree to which a structural element is displaced under a load.

How to calculate Length of Column given Initial Deflection at Distance X from end A?

The Length of Column given Initial Deflection at Distance X from end A formula is defined as a calculation that determines the length of a column with initial curvature, taking into account the initial deflection at a specific distance from end A, providing a crucial parameter in structural analysis and design is calculated using Length of Column = (pi*Distance of Deflection from end A)/(asin(Initial Deflection/Maximum Initial Deflection)). To calculate Length of Column given Initial Deflection at Distance X from end A, you need Distance of Deflection from end A (x), Initial Deflection (y') & Maximum Initial Deflection (C). With our tool, you need to enter the respective value for Distance of Deflection from end A, Initial Deflection & 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, Initial Deflection & Maximum Initial Deflection. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of Column = sqrt(((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Euler Load))
Length of Column = (pi*Distance of Deflection from end A)/(asin(Deflection of Column/((1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection)))

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