Euler Load given Factor of Safety Calculator

✖Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.ⓘ Crippling Load [P]			+10% -10%
✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety [f_s]			+10% -10%

✖Euler load is the compressive load at which a slender column will suddenly bend or buckle.ⓘ Euler Load given Factor of Safety [P_E]

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Euler Load given Factor of Safety Solution

STEP 0: Pre-Calculation Summary

Formula Used

Euler Load = Crippling Load/(1-(1/Factor of Safety))
P_E = P/(1-(1/f_s))
This formula uses 3 Variables

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.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

STEP 1: Convert Input(s) to Base Unit

Crippling Load: 2571.429 Newton --> 2571.429 Newton No Conversion Required
Factor of Safety: 2.8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_E = P/(1-(1/f_s)) --> 2571.429/(1-(1/2.8))

Evaluating ... ...

P_E = 4000.00066666667

STEP 3: Convert Result to Output's Unit

4000.00066666667 Newton --> No Conversion Required

FINAL ANSWER

4000.00066666667 ≈ 4000.001 Newton <-- Euler Load

(Calculation completed in 00.004 seconds)

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

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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)

Euler Load given Factor of Safety Formula

LaTeX Go

Euler Load = Crippling Load/(1-(1/Factor of Safety))
P_E = P/(1-(1/f_s))

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 Factor of Safety?

Euler Load given Factor of Safety calculator uses Euler Load = Crippling Load/(1-(1/Factor of Safety)) to calculate the Euler Load, The Euler Load given Factor of Safety formula is defined as the maximum load that a column with initial curvature can withstand without failing, taking into account the factor of safety to ensure structural integrity and prevent collapse under various loads. Euler Load is denoted by P_E symbol.

How to calculate Euler Load given Factor of Safety using this online calculator? To use this online calculator for Euler Load given Factor of Safety, enter Crippling Load (P) & Factor of Safety (f_s) and hit the calculate button. Here is how the Euler Load given Factor of Safety calculation can be explained with given input values -> 5600 = 2571.429/(1-(1/2.8)).

FAQ

What is Euler Load given Factor of Safety?

The Euler Load given Factor of Safety formula is defined as the maximum load that a column with initial curvature can withstand without failing, taking into account the factor of safety to ensure structural integrity and prevent collapse under various loads and is represented as P_E = P/(1-(1/f_s)) or Euler Load = Crippling Load/(1-(1/Factor of Safety)). Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself & Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

How to calculate Euler Load given Factor of Safety?

The Euler Load given Factor of Safety formula is defined as the maximum load that a column with initial curvature can withstand without failing, taking into account the factor of safety to ensure structural integrity and prevent collapse under various loads is calculated using Euler Load = Crippling Load/(1-(1/Factor of Safety)). To calculate Euler Load given Factor of Safety, you need Crippling Load (P) & Factor of Safety (f_s). With our tool, you need to enter the respective value for Crippling Load & Factor of Safety 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 & Factor of Safety. 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-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column))
Euler Load = Crippling Load/(1-(Maximum Initial Deflection/Deflection of Column))

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