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

✖Young's Modulus is a measure of the stiffness of a solid material, used to calculate the length of a beam under various load conditions and beam types.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of Inertia of Beam is a measure of the beam's resistance to bending under various load conditions, depending on its length and type.ⓘ Moment of Inertia of Beam [I]			+10% -10%
✖Static Deflection is the maximum displacement of a beam from its original position under various load conditions, providing values for different types of beams.ⓘ Static Deflection [δ]			+10% -10%
✖Load Attached to Free End of Constraint is the force exerted on the free end of a beam under various load conditions and beam types.ⓘ Load Attached to Free End of Constraint [W_attached]			+10% -10%

✖Length of Cantilever Beam is the distance from the fixed end to the free end of a beam under various load conditions and beam types.ⓘ Length of Beam for Cantilever Beam with Point Load at Free End [L_CB]

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

Variables Used

Length of Cantilever Beam - (Measured in Meter) - Length of Cantilever Beam is the distance from the fixed end to the free end of a beam under various load conditions and beam types.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a measure of the stiffness of a solid material, used to calculate the length of a beam under various load conditions and beam types.
Moment of Inertia of Beam - (Measured in Meter⁴ per Meter) - Moment of Inertia of Beam is a measure of the beam's resistance to bending under various load conditions, depending on its length and type.
Static Deflection - (Measured in Meter) - Static Deflection is the maximum displacement of a beam from its original position under various load conditions, providing values for different types of beams.
Load Attached to Free End of Constraint - Load Attached to Free End of Constraint is the force exerted on the free end of a beam under various load conditions and beam types.

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: 0.85 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_CB = ((3*E*I*δ)/(W_attached))^(1/3) --> ((3*15*6*0.072)/(0.85))^(1/3)

Evaluating ... ...

L_CB = 2.83852317894893

STEP 3: Convert Result to Output's Unit

2.83852317894893 Meter --> No Conversion Required

FINAL ANSWER

2.83852317894893 ≈ 2.838523 Meter <-- Length of Cantilever Beam

(Calculation completed in 00.020 seconds)

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

Length of Fixed Beam with Eccentric Point Load

LaTeX Go Length of Fixed Beam = (Eccentric Point Load for Fixed Beam*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 Simply Supported Beam with Uniformly Distributed Load

LaTeX Go Length of Simply Supported Beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(5*Load in Simply Supported Beam))^(1/4)

Length of Beam for Fixed Beam with Uniformly Distributed Load

LaTeX Go Length of Fixed Beam = ((384*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load in Fixed Beam))^(1/4)

Length of Beam for Fixed Beam with Central Point Load

LaTeX Go Length of Fixed Beam = ((192*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

LaTeX Go

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

What is Beam?

A beam is a structural element designed to support and distribute loads, primarily by resisting bending. It is typically a long, horizontal member used in construction, bridges, and frameworks to transfer loads to supports such as walls or columns. Beams are essential in providing stability and strength to structures, allowing them to bear various forces like weight, wind, or pressure. Depending on how they are supported and loaded, beams can be classified into types like simply supported, cantilever, or fixed beams.

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 Cantilever 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 Cantilever 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 Cantilever Beam is denoted by L_CB 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 -> 2.784953 = ((3*15*6*0.072)/(0.85))^(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_CB = ((3*E*I*δ)/(W_attached))^(1/3) or Length of Cantilever 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 measure of the stiffness of a solid material, used to calculate the length of a beam under various load conditions and beam types, Moment of Inertia of Beam is a measure of the beam's resistance to bending under various load conditions, depending on its length and type, Static Deflection is the maximum displacement of a beam from its original position under various load conditions, providing values for different types of beams & Load Attached to Free End of Constraint is the force exerted on the free end of a beam under various load conditions and beam types.

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 Cantilever 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 Cantilever Beam?

In this formula, Length of Cantilever Beam uses Young's Modulus, Moment of Inertia of Beam, Static Deflection & Load Attached to Free End of Constraint. We can use 1 other way(s) to calculate the same, which is/are as follows -

Length of Cantilever Beam = ((8*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load in Cantilever Beam))^(1/4)

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