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Deflection of Fixed Beam with Load at Center Formula

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Deflection of beam is the degree to which a structural element is displaced under a load (due to its deformation). Check FAQs

δ = \frac{W beam \cdot {L beam}^{3}}{192 \cdot e \cdot I}

δ - Deflection of Beam?W_beam - Width of Beam?L_beam - Beam Length?e - Elastic Modulus?I - Moment of Inertia?

Deflection of Fixed Beam with Load at Center Example

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Here is how the Deflection of Fixed Beam with Load at Center equation looks like with Values.

Here is how the Deflection of Fixed Beam with Load at Center equation looks like with Units.

Here is how the Deflection of Fixed Beam with Load at Center equation looks like.

0.1843 = \frac{18 \cdot 4800^{3}}{192 \cdot 50 \cdot 1.125}

0.1843mm = \frac{18mm \cdot {4800mm}^{3}}{192 \cdot 50Pa \cdot 1.125kg·m²}

0.1843 = \frac{18 \cdot 4800^{3}}{192 \cdot 50 \cdot 1.125}

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Strength of Materials » fx Deflection of Fixed Beam with Load at Center

Deflection of Fixed Beam with Load at Center Solution

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

FIRST Step Consider the formula

δ = \frac{W beam \cdot {L beam}^{3}}{192 \cdot e \cdot I}

Next Step Substitute values of Variables

∴

δ = \frac{18mm \cdot {4800mm}^{3}}{192 \cdot 50Pa \cdot 1.125kg·m²}

Next Step Convert Units

∴

δ = \frac{0.018m \cdot {4.8m}^{3}}{192 \cdot 50Pa \cdot 1.125kg·m²}

Next Step Prepare to Evaluate

∴

δ = \frac{0.018 \cdot {4.8}^{3}}{192 \cdot 50 \cdot 1.125}

Next Step Evaluate

∴

δ = 0.00018432m

Next Step Convert to Output's Unit

∴

δ = 0.18432mm

LAST Step Rounding Answer

∴

δ = 0.1843mm

Deflection of Fixed Beam with Load at Center Formula Elements

Variables

Deflection of Beam

Deflection of beam is the degree to which a structural element is displaced under a load (due to its deformation).

Symbol: δ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Beam

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 Load at Center?

Deflection of Fixed Beam with Load at Center evaluator uses Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia) to evaluate the Deflection of Beam, The Deflection of Fixed Beam with Load at Center formula is defined as a measure of the maximum displacement of a fixed beam from its original position when a load is applied at its center, providing insight into the beam's stress and strain behavior under various loading conditions. Deflection of Beam is denoted by δ symbol.

How to evaluate Deflection of Fixed Beam with Load at Center using this online evaluator? To use this online evaluator for Deflection of Fixed Beam with Load at Center, 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 Load at Center

What is the formula to find Deflection of Fixed Beam with Load at Center?

The formula of Deflection of Fixed Beam with Load at Center is expressed as Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia). Here is an example- 184.32 = (0.018*4.8^3)/(192*50*1.125).

How to calculate Deflection of Fixed Beam with Load at Center?

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 Load at Center using the formula - Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia).

Can the Deflection of Fixed Beam with Load at Center be negative?

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

Which unit is used to measure Deflection of Fixed Beam with Load at Center?

Deflection of Fixed Beam with Load at Center 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 Load at Center can be measured.

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Deflection of Fixed Beam with Load at Center Formula

Deflection of Fixed Beam with Load at Center Example

Deflection of Fixed Beam with Load at Center Solution

Deflection of Fixed Beam with Load at Center Formula Elements

Other formulas in Stress and Strain category

How to Evaluate Deflection of Fixed Beam with Load at Center?

FAQs on Deflection of Fixed Beam with Load at Center

Variable Name