Final Deflection at Distance X from end A of Column Calculator

✖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%
✖Distance of Deflection from end A is the distance x of deflection from end A.ⓘ Distance of Deflection from end A [x]			+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%

✖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.ⓘ Final Deflection at Distance X from end A of Column [δ_c]

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Final Deflection at Distance X from end A of Column Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
Distance of Deflection from end A - (Measured in Meter) - Distance of Deflection from end A is the distance x of deflection from end A.
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

Crippling Load: 2571.429 Newton --> 2571.429 Newton No Conversion Required
Euler Load: 4000 Newton --> 4000 Newton No Conversion Required
Maximum Initial Deflection: 300 Millimeter --> 0.3 Meter (Check conversion here)
Distance of Deflection from end A: 35 Millimeter --> 0.035 Meter (Check conversion here)
Length of Column: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ_c = (1/(1-(P/P_E)))*C*sin((pi*x)/l) --> (1/(1-(2571.429/4000)))*0.3*sin((pi*0.035)/5)

Evaluating ... ...

δ_c = 0.0184710814590287

STEP 3: Convert Result to Output's Unit

0.0184710814590287 Meter -->18.4710814590287 Millimeter (Check conversion here)

FINAL ANSWER

18.4710814590287 ≈ 18.47108 Millimeter <-- Deflection 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 » Final Deflection at Distance X from end A of Column

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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)

Final Deflection at Distance X from end A of Column Formula

LaTeX Go

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

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 Final Deflection at Distance X from end A of Column?

Final Deflection at Distance X from end A of Column calculator 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 calculate 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 calculate Final Deflection at Distance X from end A of Column using this online calculator? To use this online calculator 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. Here is how the Final Deflection at Distance X from end A of Column calculation can be explained with given input values -> 18471.08 = (1/(1-(2571.429/4000)))*0.3*sin((pi*0.035)/5).

FAQ

What is Final Deflection at Distance X from end A 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 and is represented as δ_c = (1/(1-(P/P_E)))*C*sin((pi*x)/l) or Deflection of Column = (1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column). 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, Distance of Deflection from end A is the distance x of deflection from end A & 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 Final Deflection at Distance X from end A 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 is calculated using Deflection of Column = (1/(1-(Crippling Load/Euler Load)))*Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column). To calculate Final Deflection at Distance X from end A of Column, you need Crippling Load (P), Euler Load (P_E), Maximum Initial Deflection (C), Distance of Deflection from end A (x) & Length of Column (l). With our tool, you need to enter the respective value for Crippling Load, Euler Load, Maximum Initial Deflection, Distance of Deflection from end A & 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 Deflection of Column?

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

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

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