Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged Calculator

✖Modulus of Elasticity of Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.ⓘ Modulus of Elasticity of Column [E]			+10% -10%
✖Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia Column [I]			+10% -10%
✖Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.ⓘ Column Crippling Load [P]			+10% -10%

✖Column Length 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 Crippling Load if One End of Column is Fixed and Other is Hinged [l]

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Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged

Formula

`"l" = sqrt((2*pi^2*"E"*"I")/("P"))`

Example

`"1972.56mm"=sqrt((2*pi^2*"10.56MPa"*"5600cm⁴")/("3kN"))`

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Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged Solution

STEP 0: Pre-Calculation Summary

Formula Used

Column Length = sqrt((2*pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load))
l = sqrt((2*pi^2*E*I)/(P))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Column Length - (Measured in Meter) - Column Length is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.
Modulus of Elasticity of Column - (Measured in Pascal) - Modulus of Elasticity of Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it.
Moment of Inertia Column - (Measured in Meter⁴) - Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis.
Column Crippling Load - (Measured in Newton) - Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

STEP 1: Convert Input(s) to Base Unit

Modulus of Elasticity of Column: 10.56 Megapascal --> 10560000 Pascal (Check conversion here)
Moment of Inertia Column: 5600 Centimeter⁴ --> 5.6E-05 Meter⁴ (Check conversion here)
Column Crippling Load: 3 Kilonewton --> 3000 Newton (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l = sqrt((2*pi^2*E*I)/(P)) --> sqrt((2*pi^2*10560000*5.6E-05)/(3000))

Evaluating ... ...

l = 1.97255997097312

STEP 3: Convert Result to Output's Unit

1.97255997097312 Meter -->1972.55997097312 Millimeter (Check conversion here)

FINAL ANSWER

1972.55997097312 ≈ 1972.56 Millimeter <-- Column Length

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Column And Struts » Expressions For Crippling Load » One End of Column is Fixed and Other is Hinged » Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged

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< 9 One End of Column is Fixed and Other is Hinged Calculators

Deflection at Section given Moment at Section if One End of Column is Fixed and Other is Hinged

Go Deflection at Section = (-Moment of Section+Horizontal Reaction*(Column Length-Distance b/w Fixed End and Deflection Point))/Column Crippling Load

Crippling Load given Moment at Section if One End of Column is Fixed and Other is Hinged

Go Column Crippling Load = (-Moment of Section+Horizontal Reaction*(Column Length-Distance b/w Fixed End and Deflection Point))/Deflection at Section

Horizontal Reaction given Moment at Section if One End of Column is Fixed and Other is Hinged

Go Horizontal Reaction = (Moment of Section+Column Crippling Load*Deflection at Section)/(Column Length-Distance b/w Fixed End and Deflection Point)

Moment at Section if One End of Column is Fixed and Other is Hinged

Go Moment of Section = -Column Crippling Load*Deflection at Section+Horizontal Reaction*(Column Length-Distance b/w Fixed End and Deflection Point)

Length of Column given Moment at Section if One End of Column is Fixed and Other is Hinged

Go Column Length = (Moment of Section+Column Crippling Load*Deflection at Section)/Horizontal Reaction+Distance b/w Fixed End and Deflection Point

Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged

Go Column Length = sqrt((2*pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load))

Modulus of Elasticity given Crippling Load if One End of Column is Fixed and Other is Hinged

Go Modulus of Elasticity of Column = (Column Crippling Load*Column Length^2)/(2*pi^2*Moment of Inertia Column)

Moment of Inertia given Crippling Load if One End of Column is Fixed and Other is Hinged

Go Moment of Inertia Column = (Column Crippling Load*Column Length^2)/(2*pi^2*Modulus of Elasticity of Column)

Crippling Load if One End of Column is Fixed and Other is Hinged

Go Column Crippling Load = (2*pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Length^2)

Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged Formula

Column Length = sqrt((2*pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load))
l = sqrt((2*pi^2*E*I)/(P))

What is meant by effective length of a column also define slenderness ratio?

The effective length of the column is the length of an equivalent column of the same material and cross-sectional area with hinged ends and having the value of the crippling load equal to that of the given column. The least radius of gyration is the radius of gyration where the least moment of inertia is considered.

How to Calculate Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged?

Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged calculator uses Column Length = sqrt((2*pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)) to calculate the Column Length, The Length of column given crippling load if one end of column is fixed and other is hinged formula is defined as the distance between two points where a column gets its fixity of support so its movement is restrained in all directions. Column Length is denoted by l symbol.

How to calculate Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged using this online calculator? To use this online calculator for Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged, enter Modulus of Elasticity of Column (E), Moment of Inertia Column (I) & Column Crippling Load (P) and hit the calculate button. Here is how the Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged calculation can be explained with given input values -> 2E+6 = sqrt((2*pi^2*10560000*5.6E-05)/(3000)).

FAQ

What is Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged?

The Length of column given crippling load if one end of column is fixed and other is hinged formula is defined as the distance between two points where a column gets its fixity of support so its movement is restrained in all directions and is represented as l = sqrt((2*pi^2*E*I)/(P)) or Column Length = sqrt((2*pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)). Modulus of Elasticity of Column is a quantity that measures an object or substance's resistance to being deformed elastically when stress is applied to it, Moment of Inertia Column is the measure of the resistance of a body to angular acceleration about a given axis & Column Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

How to calculate Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged?

The Length of column given crippling load if one end of column is fixed and other is hinged formula is defined as the distance between two points where a column gets its fixity of support so its movement is restrained in all directions is calculated using Column Length = sqrt((2*pi^2*Modulus of Elasticity of Column*Moment of Inertia Column)/(Column Crippling Load)). To calculate Length of Column given Crippling Load if One End of Column is Fixed and Other is Hinged, you need Modulus of Elasticity of Column (E), Moment of Inertia Column (I) & Column Crippling Load (P). With our tool, you need to enter the respective value for Modulus of Elasticity of Column, Moment of Inertia Column & Column Crippling Load 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 Column Length?

In this formula, Column Length uses Modulus of Elasticity of Column, Moment of Inertia Column & Column Crippling Load. We can use 1 other way(s) to calculate the same, which is/are as follows -

Column Length = (Moment of Section+Column Crippling Load*Deflection at Section)/Horizontal Reaction+Distance b/w Fixed End and Deflection Point

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