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

GoLength of Beam for Cantilever Beam with Uniformly Distributed Load Formula

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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. Check FAQs

L CB = {(\frac{3 \cdot E \cdot I \cdot δ}{W attached})}^{\frac{1}{3}}

L_CB - Length of Cantilever Beam?E - Young's Modulus?I - Moment of Inertia of Beam?δ - Static Deflection?W_attached - Load Attached to Free End of Constraint?

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

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Here is how the Length of Beam for Cantilever Beam with Point Load at Free End equation looks like with Values.

Here is how the Length of Beam for Cantilever Beam with Point Load at Free End equation looks like with Units.

Here is how the Length of Beam for Cantilever Beam with Point Load at Free End equation looks like.

2.8385 = {(\frac{3 \cdot 15 \cdot 6 \cdot 0.072}{0.85})}^{\frac{1}{3}}

2.8385m = {(\frac{3 \cdot 15N/m \cdot 6m⁴/m \cdot 0.072m}{0.85})}^{\frac{1}{3}}

2.8385 = {(\frac{3 \cdot 15 \cdot 6 \cdot 0.072}{0.85})}^{\frac{1}{3}}

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

Follow our step by step solution on how to calculate Length of Beam for Cantilever Beam with Point Load at Free End?

FIRST Step Consider the formula

L CB = {(\frac{3 \cdot E \cdot I \cdot δ}{W attached})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

L CB = {(\frac{3 \cdot 15N/m \cdot 6m⁴/m \cdot 0.072m}{0.85})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

L CB = {(\frac{3 \cdot 15 \cdot 6 \cdot 0.072}{0.85})}^{\frac{1}{3}}

Next Step Evaluate

∴

L CB = 2.83852317894893m

LAST Step Rounding Answer

∴

L CB = 2.8385m

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

Variables

Length of Cantilever Beam

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.

Symbol: L_CB

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Cantilever Beam

Young's Modulus

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.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Moment of Inertia of Beam

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.

Symbol: I

Measurement: Moment of Inertia per Unit LengthUnit: m⁴/m

Note: Value should be greater than 0.

Formulas to find Moment of Inertia of Beam

Static Deflection

Static Deflection is the maximum displacement of a beam from its original position under various load conditions, providing values for different types of beams.

Symbol: δ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Static Deflection

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.

Symbol: W_attached

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load Attached to Free End of Constraint

Other Formulas to find Length of Cantilever Beam

Go Length of Beam for Cantilever Beam with Uniformly Distributed Load

L CB = {(\frac{8 \cdot E \cdot I \cdot δ}{w CB})}^{\frac{1}{4}}

Other formulas in Values of length of beam for the various types of beams and under various load conditions category

Go Length of Beam for Fixed Beam with Uniformly Distributed Load

L FB = {(\frac{384 \cdot E \cdot I \cdot δ}{w FB})}^{\frac{1}{4}}

Go Length of Beam for Fixed Beam with Central Point Load

L FB = {(\frac{192 \cdot E \cdot I \cdot δ}{w c})}^{\frac{1}{3}}

Go Length of Fixed Beam with Eccentric Point Load

L FB = \frac{w e \cdot a^{3} \cdot b^{3}}{3 \cdot E \cdot I \cdot δ}

Go Length of Beam for Simply Supported Beam with Uniformly Distributed Load

L SSB = {(\frac{384 \cdot E \cdot I \cdot δ}{5 \cdot w SSB})}^{\frac{1}{4}}

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

Length of Beam for Cantilever Beam with Point Load at Free End evaluator 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 evaluate 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 evaluate Length of Beam for Cantilever Beam with Point Load at Free End using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Length of Beam for Cantilever Beam with Point Load at Free End?

The formula of Length of Beam for Cantilever Beam with Point Load at Free End is expressed as Length of Cantilever Beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3). Here is an example- 2.784953 = ((3*15*6*0.072)/(0.85))^(1/3).

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

With Young's Modulus (E), Moment of Inertia of Beam (I), Static Deflection (δ) & Load Attached to Free End of Constraint (W_attached) we can find Length of Beam for Cantilever Beam with Point Load at Free End using the formula - Length of Cantilever Beam = ((3*Young's Modulus*Moment of Inertia of Beam*Static Deflection)/(Load Attached to Free End of Constraint))^(1/3).

What are the other ways to Calculate Length of Cantilever Beam?

Here are the different ways to Calculate Length of Cantilever Beam-

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

Can the Length of Beam for Cantilever Beam with Point Load at Free End be negative?

No, the Length of Beam for Cantilever Beam with Point Load at Free End, measured in Length cannot be negative.

Which unit is used to measure Length of Beam for Cantilever Beam with Point Load at Free End?

Length of Beam for Cantilever Beam with Point Load at Free End is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length of Beam for Cantilever Beam with Point Load at Free End can be measured.

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

​GoLength of Beam for Cantilever Beam with Uniformly Distributed Load Formula

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

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

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

Other Formulas to find Length of Cantilever Beam

Other formulas in Values of length of beam for the various types of beams and under various load conditions category

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

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

Variable Name

GoLength of Beam for Cantilever Beam with Uniformly Distributed Load Formula