Euler Load given 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%
✖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.ⓘ Deflection of Column [δ_c]			+10% -10%

✖Euler load is the compressive load at which a slender column will suddenly bend or buckle.ⓘ Euler Load given Final Deflection at Distance X from end A of Column [P_E]

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Euler Load given Final Deflection at Distance X from end A of Column Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Euler Load - (Measured in Newton) - Euler load is the compressive load at which a slender column will suddenly bend or buckle.
Crippling Load - (Measured in Newton) - Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Crippling Load: 2571.429 Newton --> 2571.429 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)
Deflection of Column: 18.47108 Millimeter --> 0.01847108 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_E = P/(1-(C*sin((pi*x)/l)/δ_c)) --> 2571.429/(1-(0.3*sin((pi*0.035)/5)/0.01847108))

Evaluating ... ...

P_E = 4000.00017553303

STEP 3: Convert Result to Output's Unit

4000.00017553303 Newton --> No Conversion Required

FINAL ANSWER

4000.00017553303 ≈ 4000 Newton <-- Euler Load

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Mechanical » Columns With Initial Curvature » Euler Load given 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)

Euler Load given Final Deflection at Distance X from end A of Column Formula

LaTeX Go

Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column))
P_E = P/(1-(C*sin((pi*x)/l)/δ_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 Euler Load given Final Deflection at Distance X from end A of Column?

Euler Load given Final Deflection at Distance X from end A of Column calculator uses Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)) to calculate the Euler Load, The Euler Load given Final Deflection at Distance X from end A of Column formula is defined as a measure of the load that a column with initial curvature can withstand, taking into account the final deflection at a specific distance from the end of the column, providing a critical value for structural integrity assessment. Euler Load is denoted by P_E symbol.

How to calculate Euler Load given Final Deflection at Distance X from end A of Column using this online calculator? To use this online calculator for Euler Load given Final Deflection at Distance X from end A of Column, enter Crippling Load (P), Maximum Initial Deflection (C), Distance of Deflection from end A (x), Length of Column (l) & Deflection of Column (δ_c) and hit the calculate button. Here is how the Euler Load given Final Deflection at Distance X from end A of Column calculation can be explained with given input values -> 5710.916 = 2571.429/(1-(0.3*sin((pi*0.035)/5)/0.01847108)).

FAQ

What is Euler Load given Final Deflection at Distance X from end A of Column?

The Euler Load given Final Deflection at Distance X from end A of Column formula is defined as a measure of the load that a column with initial curvature can withstand, taking into account the final deflection at a specific distance from the end of the column, providing a critical value for structural integrity assessment and is represented as P_E = P/(1-(C*sin((pi*x)/l)/δ_c)) or Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)). Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself, 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 & 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.

How to calculate Euler Load given Final Deflection at Distance X from end A of Column?

The Euler Load given Final Deflection at Distance X from end A of Column formula is defined as a measure of the load that a column with initial curvature can withstand, taking into account the final deflection at a specific distance from the end of the column, providing a critical value for structural integrity assessment is calculated using Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)). To calculate Euler Load given Final Deflection at Distance X from end A of Column, you need Crippling Load (P), Maximum Initial Deflection (C), Distance of Deflection from end A (x), Length of Column (l) & Deflection of Column (δ_c). With our tool, you need to enter the respective value for Crippling Load, Maximum Initial Deflection, Distance of Deflection from end A, Length of Column & Deflection 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 Euler Load?

In this formula, Euler Load uses Crippling Load, Maximum Initial Deflection, Distance of Deflection from end A, Length of Column & Deflection of Column. We can use 3 other way(s) to calculate the same, which is/are as follows -

Euler Load = ((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)
Euler Load = Crippling Load/(1-(1/Factor of Safety))
Euler Load = Crippling Load/(1-(Maximum Initial Deflection/Deflection of Column))

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