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Static Deflection in Fixed Beam with Eccentric Point Load Formula

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

GoStatic Deflection for Cantilever Beam with Uniformly Distributed 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 e \cdot a^{3} \cdot b^{3}}{3 \cdot E \cdot I \cdot L fix}

δ - Static Deflection?w_e - Eccentric Point Load?a - Distance of Load from One End?b - Distance of Load from Other End?E - Young's Modulus?I - Moment of Inertia of Beam?L_fix - Length of Fixed Beam?

Static Deflection in Fixed Beam with Eccentric Point Load Example

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Here is how the Static Deflection in Fixed Beam with Eccentric Point Load equation looks like with Values.

Here is how the Static Deflection in Fixed Beam with Eccentric Point Load equation looks like with Units.

Here is how the Static Deflection in Fixed Beam with Eccentric Point Load equation looks like.

0.0702 = \frac{5.4 \cdot {2.16}^{3} \cdot {1.4}^{3}}{3 \cdot 15 \cdot 6 \cdot 7.88}

0.0702m = \frac{5.4kg \cdot {2.16m}^{3} \cdot {1.4m}^{3}}{3 \cdot 15N/m \cdot 6m⁴/m \cdot 7.88m}

0.0702 = \frac{5.4 \cdot {2.16}^{3} \cdot {1.4}^{3}}{3 \cdot 15 \cdot 6 \cdot 7.88}

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Static Deflection in Fixed Beam with Eccentric Point Load Solution

Follow our step by step solution on how to calculate Static Deflection in Fixed Beam with Eccentric Point Load?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ = \frac{5.4kg \cdot {2.16m}^{3} \cdot {1.4m}^{3}}{3 \cdot 15N/m \cdot 6m⁴/m \cdot 7.88m}

Next Step Prepare to Evaluate

∴

δ = \frac{5.4 \cdot {2.16}^{3} \cdot {1.4}^{3}}{3 \cdot 15 \cdot 6 \cdot 7.88}

Next Step Evaluate

∴

δ = 0.0701857812791878m

LAST Step Rounding Answer

∴

δ = 0.0702m

Static Deflection in Fixed Beam with Eccentric Point 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

Eccentric Point Load

Eccentric point load is the point on a beam where a load is applied at a distance from the beam's longitudinal axis.

Symbol: w_e

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Eccentric Point Load

Distance of Load from One End

Distance of load from one end is the horizontal distance of the load from one end of the beam, affecting the beam's static deflection under various load conditions.

Symbol: a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance of Load from One End

Distance of Load from Other End

Distance of load from other end is the horizontal distance from the point of application of load to the other end of the beam.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Distance of Load from Other End

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

Length of Fixed Beam

Length of Fixed Beam is the maximum deflection of a fixed beam under various load conditions, providing insight into beam's stress and deformation behavior.

Symbol: L_fix

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Fixed 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 Cantilever Beam with Uniformly Distributed Load

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

How to Evaluate Static Deflection in Fixed Beam with Eccentric Point Load?

Static Deflection in Fixed Beam with Eccentric Point Load evaluator uses Static Deflection = (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*Length of Fixed Beam) to evaluate the Static Deflection, Static Deflection in Fixed Beam with Eccentric Point Load formula is defined as a measure of the maximum displacement of a fixed beam under an eccentric point load, providing insights into the beam's deformation under various load conditions, essential for structural analysis and design. Static Deflection is denoted by δ symbol.

How to evaluate Static Deflection in Fixed Beam with Eccentric Point Load using this online evaluator? To use this online evaluator for Static Deflection in Fixed Beam with Eccentric Point Load, enter Eccentric Point Load (w_e), Distance of Load from One End (a), Distance of Load from Other End (b), Young's Modulus (E), Moment of Inertia of Beam (I) & Length of Fixed Beam (L_fix) and hit the calculate button.

FAQs on Static Deflection in Fixed Beam with Eccentric Point Load

What is the formula to find Static Deflection in Fixed Beam with Eccentric Point Load?

The formula of Static Deflection in Fixed Beam with Eccentric Point Load is expressed as Static Deflection = (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*Length of Fixed Beam). Here is an example- 0.445726 = (5.4*2.16^3*1.4^3)/(3*15*6*7.88).

How to calculate Static Deflection in Fixed Beam with Eccentric Point Load?

With Eccentric Point Load (w_e), Distance of Load from One End (a), Distance of Load from Other End (b), Young's Modulus (E), Moment of Inertia of Beam (I) & Length of Fixed Beam (L_fix) we can find Static Deflection in Fixed Beam with Eccentric Point Load using the formula - Static Deflection = (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*Length of Fixed 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=(Load per unit Length*Length of Cantilever Beam^4)/(8*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)

Can the Static Deflection in Fixed Beam with Eccentric Point Load be negative?

No, the Static Deflection in Fixed Beam with Eccentric Point Load, measured in Length cannot be negative.

Which unit is used to measure Static Deflection in Fixed Beam with Eccentric Point Load?

Static Deflection in Fixed Beam with Eccentric Point 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 in Fixed Beam with Eccentric Point Load can be measured.

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Static Deflection in Fixed Beam with Eccentric Point Load Formula

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

​GoStatic Deflection for Cantilever Beam with Uniformly Distributed Load Formula

Static Deflection in Fixed Beam with Eccentric Point Load Example

Static Deflection in Fixed Beam with Eccentric Point Load Solution

Static Deflection in Fixed Beam with Eccentric Point Load Formula Elements

Other Formulas to find Static Deflection

How to Evaluate Static Deflection in Fixed Beam with Eccentric Point Load?

FAQs on Static Deflection in Fixed Beam with Eccentric Point Load

Variable Name

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

GoStatic Deflection for Cantilever Beam with Uniformly Distributed Load Formula