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Deflection of Fixed Beam with Uniformly Distributed Load Formula

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Deflection of Fixed Beam with UDL is the deflection in the fixed beam caused due to the uniformly distributed load. Check FAQs

d = \frac{W beam \cdot {L beam}^{4}}{384 \cdot e \cdot I}

d - Deflection of Fixed Beam with UDL?W_beam - Width of Beam?L_beam - Beam Length?e - Elastic Modulus?I - Moment of Inertia?

Deflection of Fixed Beam with Uniformly Distributed Load Example

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Here is how the Deflection of Fixed Beam with Uniformly Distributed Load equation looks like with Values.

Here is how the Deflection of Fixed Beam with Uniformly Distributed Load equation looks like with Units.

Here is how the Deflection of Fixed Beam with Uniformly Distributed Load equation looks like.

0.4424 = \frac{18 \cdot 4800^{4}}{384 \cdot 50 \cdot 1.125}

0.4424mm = \frac{18mm \cdot {4800mm}^{4}}{384 \cdot 50Pa \cdot 1.125kg·m²}

0.4424 = \frac{18 \cdot 4800^{4}}{384 \cdot 50 \cdot 1.125}

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Deflection of Fixed Beam with Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate Deflection of Fixed Beam with Uniformly Distributed Load?

FIRST Step Consider the formula

d = \frac{W beam \cdot {L beam}^{4}}{384 \cdot e \cdot I}

Next Step Substitute values of Variables

∴

d = \frac{18mm \cdot {4800mm}^{4}}{384 \cdot 50Pa \cdot 1.125kg·m²}

Next Step Convert Units

∴

d = \frac{0.018m \cdot {4.8m}^{4}}{384 \cdot 50Pa \cdot 1.125kg·m²}

Next Step Prepare to Evaluate

∴

d = \frac{0.018 \cdot {4.8}^{4}}{384 \cdot 50 \cdot 1.125}

Next Step Evaluate

∴

d = 0.000442368m

Next Step Convert to Output's Unit

∴

d = 0.442368mm

LAST Step Rounding Answer

∴

d = 0.4424mm

Deflection of Fixed Beam with Uniformly Distributed Load Formula Elements

Variables

Deflection of Fixed Beam with UDL

Deflection of Fixed Beam with UDL is the deflection in the fixed beam caused due to the uniformly distributed load.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Fixed Beam with UDL

Width of Beam

Width of Beam is the horizontal measurement taken perpendicular to the length of beam.

Symbol: W_beam

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Width of Beam

Beam Length

Beam Length is the center to center distance between the supports or the effective length of the beam.

Symbol: L_beam

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Beam Length

Elastic Modulus

The Elastic Modulus is a fundamental property that quantifies the stiffness of a material. It is defined as the ratio of stress to strain within the elastic range of a material.

Symbol: e

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Elastic Modulus

Moment of Inertia

Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

Other formulas in Stress and Strain category

Go Elongation Circular Tapered Bar

Δ c = \frac{4 \cdot W load \cdot L bar}{π \cdot D 1 \cdot D 2 \cdot e}

Go Moment of Inertia for Hollow Circular Shaft

J h = \frac{π}{32} \cdot ({d ho}^{4} - {d hi}^{4})

Go Moment of Inertia about Polar Axis

J = \frac{π \cdot {d s}^{4}}{32}

Go Elongation of Prismatic Bar due to its Own Weight

Δ p = \frac{W load \cdot L bar}{2 \cdot A \cdot e}

How to Evaluate Deflection of Fixed Beam with Uniformly Distributed Load?

Deflection of Fixed Beam with Uniformly Distributed Load evaluator uses Deflection of Fixed Beam with UDL = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia) to evaluate the Deflection of Fixed Beam with UDL, The Deflection of Fixed Beam with Uniformly Distributed Load formula is defined as a measure of the maximum displacement of a fixed beam under a uniformly distributed load, providing insight into the beam's stress and strain characteristics, and is essential in structural analysis and design. Deflection of Fixed Beam with UDL is denoted by d symbol.

How to evaluate Deflection of Fixed Beam with Uniformly Distributed Load using this online evaluator? To use this online evaluator for Deflection of Fixed Beam with Uniformly Distributed Load, enter Width of Beam (W_beam), Beam Length (L_beam), Elastic Modulus (e) & Moment of Inertia (I) and hit the calculate button.

FAQs on Deflection of Fixed Beam with Uniformly Distributed Load

What is the formula to find Deflection of Fixed Beam with Uniformly Distributed Load?

The formula of Deflection of Fixed Beam with Uniformly Distributed Load is expressed as Deflection of Fixed Beam with UDL = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia). Here is an example- 442.368 = (0.018*4.8^4)/(384*50*1.125).

How to calculate Deflection of Fixed Beam with Uniformly Distributed Load?

With Width of Beam (W_beam), Beam Length (L_beam), Elastic Modulus (e) & Moment of Inertia (I) we can find Deflection of Fixed Beam with Uniformly Distributed Load using the formula - Deflection of Fixed Beam with UDL = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia).

Can the Deflection of Fixed Beam with Uniformly Distributed Load be negative?

No, the Deflection of Fixed Beam with Uniformly Distributed Load, measured in Length cannot be negative.

Which unit is used to measure Deflection of Fixed Beam with Uniformly Distributed Load?

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

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Deflection of Fixed Beam with Uniformly Distributed Load Formula

Deflection of Fixed Beam with Uniformly Distributed Load Example

Deflection of Fixed Beam with Uniformly Distributed Load Solution

Deflection of Fixed Beam with Uniformly Distributed Load Formula Elements

Other formulas in Stress and Strain category

How to Evaluate Deflection of Fixed Beam with Uniformly Distributed Load?

FAQs on Deflection of Fixed Beam with Uniformly Distributed Load

Variable Name