Length of Beam for Cantilever Beam with Point Load at Free End Calculator

✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of Inertia of Beam is a quantitative measure of the rotational inertia of a body.ⓘ Moment of Inertia of Beam [I]			+10% -10%
✖Static deflection is the extension or compression of the constraint.ⓘ Static Deflection [δ]			+10% -10%
✖Load attached to free end of constraint is a weight or source of pressure.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%

✖Length of beam between inflection points.ⓘ Length of Beam for Cantilever Beam with Point Load at Free End [L]

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Formula

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Length of Beam for Cantilever Beam with Point Load at Free End

Formula

`"L" = ((3*"E"*"I"*"δ")/("W"_{"attached"}))^(1/3)`

Example

`"3.343728m"=((3*"15N/m"*"6m⁴/m"*"0.072m")/("0.52kg"))^(1/3)`

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Length of Beam for Cantilever Beam with Point Load at Free End Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3)
L = ((3*E*I*δ)/(W_attached))^(1/3)
This formula uses 5 Variables

Variables Used

Length of beam - (Measured in Meter) - Length of beam between inflection points.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Moment of Inertia of Beam - (Measured in Meter⁴ per Meter) - Moment of Inertia of Beam is a quantitative measure of the rotational inertia of a body.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.
Load Attached to Free End of Constraint - (Measured in Kilogram) - Load attached to free end of constraint is a weight or source of pressure.

STEP 1: Convert Input(s) to Base Unit

Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of Inertia of Beam: 6 Meter⁴ per Meter --> 6 Meter⁴ per Meter No Conversion Required
Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required
Load Attached to Free End of Constraint: 0.52 Kilogram --> 0.52 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L = ((3*E*I*δ)/(W_attached))^(1/3) --> ((3*15*6*0.072)/(0.52))^(1/3)

Evaluating ... ...

L = 3.34372823387718

STEP 3: Convert Result to Output's Unit

3.34372823387718 Meter --> No Conversion Required

FINAL ANSWER

3.34372823387718 ≈ 3.343728 Meter <-- Length of beam

(Calculation completed in 00.007 seconds)

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< 8 Values of length of beam for the various types of beams and under various load conditions Calculators

Length of Simply Supported Beam with Eccentric Point Load

Go Length of beam = (Eccentric point load*Distance of load from one end^2*Distance of load from other end^2)/(3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)

Length of Fixed Beam with Eccentric Point Load

Go Length of beam = (Eccentric point load*Distance of load from one end^3*Distance of load from other end^3)/(3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)

Length of Beam for Cantilever Beam with Point Load at Free End

Go Length of beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3)

Length of Beam for Simply Supported Beam with Uniformly Distributed Load

Go Length of beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(5*Load per unit length))^(1/4)

Length of Beam for Fixed Beam with Uniformly Distributed Load

Go Length of beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load per unit length))^(1/4)

Length of Beam for Cantilever Beam with Uniformly Distributed Load

Go Length of beam = ((8*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load per unit length))^(1/4)

Length of Beam for Fixed Beam with Central Point Load

Go Length of beam = ((192*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)

Length of Beam for Simply Supported Beam with Central Point Load

Go Length of beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)

Length of Beam for Cantilever Beam with Point Load at Free End Formula

Length of beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3)
L = ((3*E*I*δ)/(W_attached))^(1/3)

What is beam and column?

Communally a horizontal member of a structure that resists transverse load is called a beam. Communally a vertical member of a structure that resists axial/eccentric load is called a column. Beam is basically carried or resists bending and shear force. Column is basically carried or resists compression load.

How to Calculate Length of Beam for Cantilever Beam with Point Load at Free End?

Length of Beam for Cantilever Beam with Point Load at Free End calculator uses Length of beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3) to calculate the Length of beam, The Length of beam for cantilever beam with point load at free end formula is simply the total length of the member. Length of beam is denoted by L symbol.

How to calculate Length of Beam for Cantilever Beam with Point Load at Free End using this online calculator? To use this online calculator for Length of Beam for Cantilever Beam with Point Load at Free End, enter Young's Modulus (E), Moment of Inertia of Beam (I), Static Deflection (δ) & Load Attached to Free End of Constraint (W_attached) and hit the calculate button. Here is how the Length of Beam for Cantilever Beam with Point Load at Free End calculation can be explained with given input values -> 3.343728 = ((3*15*6*0.072)/(0.52))^(1/3).

FAQ

What is Length of Beam for Cantilever Beam with Point Load at Free End?

The Length of beam for cantilever beam with point load at free end formula is simply the total length of the member and is represented as L = ((3*E*I*δ)/(W_attached))^(1/3) or Length of beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3). Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Moment of Inertia of Beam is a quantitative measure of the rotational inertia of a body, Static deflection is the extension or compression of the constraint & Load attached to free end of constraint is a weight or source of pressure.

How to calculate Length of Beam for Cantilever Beam with Point Load at Free End?

The Length of beam for cantilever beam with point load at free end formula is simply the total length of the member is calculated using Length of beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3). To calculate Length of Beam for Cantilever Beam with Point Load at Free End, you need Young's Modulus (E), Moment of Inertia of Beam (I), Static Deflection (δ) & Load Attached to Free End of Constraint (W_attached). With our tool, you need to enter the respective value for Young's Modulus, Moment of Inertia of Beam, Static Deflection & Load Attached to Free End of Constraint 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 beam?

In this formula, Length of beam uses Young's Modulus, Moment of Inertia of Beam, Static Deflection & Load Attached to Free End of Constraint. We can use 7 other way(s) to calculate the same, which is/are as follows -

Length of beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load per unit length))^(1/4)
Length of beam = ((192*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)
Length of beam = (Eccentric point load*Distance of load from one end^3*Distance of load from other end^3)/(3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)
Length of beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(5*Load per unit length))^(1/4)
Length of beam = ((48*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Central point load))^(1/3)
Length of beam = (Eccentric point load*Distance of load from one end^2*Distance of load from other end^2)/(3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)
Length of beam = ((8*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load per unit length))^(1/4)

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