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Static Deflection for Cantilever Beam with Uniformly Distributed Load Formula

GoStatic Deflection for Cantilever Beam with Point Load at Free End Formula

GoStatic Deflection for Simply Supported Beam with Central Point Load Formula

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Static Deflection is the maximum displacement of a beam from its original position under various load conditions and types of beams. Check FAQs

δ = \frac{w \cdot {L cant}^{4}}{8 \cdot E \cdot I}

δ - Static Deflection?w - Load per unit Length?L_cant - Length of Cantilever Beam?E - Young's Modulus?I - Moment of Inertia of Beam?

Static Deflection for Cantilever Beam with Uniformly Distributed Load Example

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Here is how the Static Deflection for Cantilever Beam with Uniformly Distributed Load equation looks like with Values.

Here is how the Static Deflection for Cantilever Beam with Uniformly Distributed Load equation looks like with Units.

Here is how the Static Deflection for Cantilever Beam with Uniformly Distributed Load equation looks like.

0.7031 = \frac{0.81 \cdot 5^{4}}{8 \cdot 15 \cdot 6}

0.7031m = \frac{0.81 \cdot {5m}^{4}}{8 \cdot 15N/m \cdot 6m⁴/m}

0.7031 = \frac{0.81 \cdot 5^{4}}{8 \cdot 15 \cdot 6}

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Static Deflection for Cantilever Beam with Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate Static Deflection for Cantilever Beam with Uniformly Distributed Load?

FIRST Step Consider the formula

δ = \frac{w \cdot {L cant}^{4}}{8 \cdot E \cdot I}

Next Step Substitute values of Variables

∴

δ = \frac{0.81 \cdot {5m}^{4}}{8 \cdot 15N/m \cdot 6m⁴/m}

Next Step Prepare to Evaluate

∴

δ = \frac{0.81 \cdot 5^{4}}{8 \cdot 15 \cdot 6}

Next Step Evaluate

∴

δ = 0.703125m

LAST Step Rounding Answer

∴

δ = 0.7031m

Static Deflection for Cantilever Beam with Uniformly Distributed Load Formula Elements

Variables

Static Deflection

Static Deflection is the maximum displacement of a beam from its original position under various load conditions and types of beams.

Symbol: δ

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Static Deflection

Load per unit Length

Load per unit length is the amount of load applied per unit length of a beam, used to calculate static deflection under various load conditions.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit Length

Length of Cantilever Beam

Length of Cantilever Beam is the maximum downward displacement of a cantilever beam under various load conditions, affecting its structural integrity and stability.

Symbol: L_cant

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 and is used to calculate the static deflection of beams under various load conditions.

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, providing insight into its structural behavior.

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

Other Formulas to find Static Deflection

Go Static Deflection for Cantilever Beam with Point Load at Free End

δ = \frac{W attached \cdot {L cant}^{3}}{3 \cdot E \cdot I}

Go Static Deflection for Simply Supported Beam with Central Point Load

δ = \frac{w c \cdot {L SS}^{3}}{48 \cdot E \cdot I}

Go Static Deflection for Simply Supported Beam with Eccentric Point Load

δ = \frac{w e \cdot a^{2} \cdot b^{2}}{3 \cdot E \cdot I \cdot L SS}

Go Static Deflection for Simply Supported Beam with Uniformly Distributed Load

δ = \frac{5 \cdot w \cdot {L SS}^{4}}{384 \cdot E \cdot J}

How to Evaluate Static Deflection for Cantilever Beam with Uniformly Distributed Load?

Static Deflection for Cantilever Beam with Uniformly Distributed Load evaluator uses Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam) to evaluate the Static Deflection, Static Deflection for Cantilever Beam with Uniformly Distributed Load formula is defined as a measure of the maximum displacement of a cantilever beam under a uniformly distributed load, providing insight into the beam's structural integrity and ability to withstand external forces. Static Deflection is denoted by δ symbol.

How to evaluate Static Deflection for Cantilever Beam with Uniformly Distributed Load using this online evaluator? To use this online evaluator for Static Deflection for Cantilever Beam with Uniformly Distributed Load, enter Load per unit Length (w), Length of Cantilever Beam (L_cant), Young's Modulus (E) & Moment of Inertia of Beam (I) and hit the calculate button.

FAQs on Static Deflection for Cantilever Beam with Uniformly Distributed Load

What is the formula to find Static Deflection for Cantilever Beam with Uniformly Distributed Load?

The formula of Static Deflection for Cantilever Beam with Uniformly Distributed Load is expressed as Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam). Here is an example- 0.703125 = (0.81*5^4)/(8*15*6).

How to calculate Static Deflection for Cantilever Beam with Uniformly Distributed Load?

With Load per unit Length (w), Length of Cantilever Beam (L_cant), Young's Modulus (E) & Moment of Inertia of Beam (I) we can find Static Deflection for Cantilever Beam with Uniformly Distributed Load using the formula - Static Deflection = (Load per unit Length*Length of Cantilever Beam^4)/(8*Young's Modulus*Moment of Inertia of Beam).

What are the other ways to Calculate Static Deflection?

Here are the different ways to Calculate Static Deflection-

Static Deflection=(Load Attached to Free End of Constraint*Length of Cantilever Beam^3)/(3*Young's Modulus*Moment of Inertia of Beam)
Static Deflection=(Central Point Load*Length of Simply Supported Beam^3)/(48*Young's Modulus*Moment of Inertia of Beam)
Static Deflection=(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*Length of Simply Supported Beam)

Can the Static Deflection for Cantilever Beam with Uniformly Distributed Load be negative?

No, the Static Deflection for Cantilever Beam with Uniformly Distributed Load, measured in Length cannot be negative.

Which unit is used to measure Static Deflection for Cantilever Beam with Uniformly Distributed Load?

Static Deflection for Cantilever Beam with Uniformly Distributed Load is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Static Deflection for Cantilever Beam with Uniformly Distributed Load can be measured.

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Static Deflection for Cantilever Beam with Uniformly Distributed Load Formula

​GoStatic Deflection for Cantilever Beam with Point Load at Free End Formula

​GoStatic Deflection for Simply Supported Beam with Central Point Load Formula

Static Deflection for Cantilever Beam with Uniformly Distributed Load Example

Static Deflection for Cantilever Beam with Uniformly Distributed Load Solution

Static Deflection for Cantilever Beam with Uniformly Distributed Load Formula Elements

Other Formulas to find Static Deflection

How to Evaluate Static Deflection for Cantilever Beam with Uniformly Distributed Load?

FAQs on Static Deflection for Cantilever Beam with Uniformly Distributed Load

Variable Name

GoStatic Deflection for Cantilever Beam with Point Load at Free End Formula

GoStatic Deflection for Simply Supported Beam with Central Point Load Formula