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Deflection of Fixed Beam with Load at Center Calculator

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Stress and Strain Strain Stress

✖Width of Beam is the horizontal measurement taken perpendicular to the length of beam.ⓘ Width of Beam [W_beam]			+10% -10%
✖Beam Length is the center to center distance between the supports or the effective length of the beam.ⓘ Beam Length [L_beam]			+10% -10%
✖The Elastic Modulus is the ratio of Stress to Strain.ⓘ Elastic Modulus [e]			+10% -10%
✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%

✖Deflection of beam is the degree to which a structural element is displaced under a load (due to its deformation).ⓘ Deflection of Fixed Beam with Load at Center [δ]

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Formula

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Deflection of Fixed Beam with Load at Center

Formula

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

Example

0.18432 mm = \frac{18 mm \cdot {4800 mm}^{3}}{192 \cdot 50 Pa \cdot 1.125 kg·m²}

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Deflection of Fixed Beam with Load at Center Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia)
δ = (W_beam*L_beam^3)/(192*e*I)
This formula uses 5 Variables

Variables Used

Deflection of Beam - (Measured in Meter) - Deflection of beam is the degree to which a structural element is displaced under a load (due to its deformation).
Width of Beam - (Measured in Meter) - Width of Beam is the horizontal measurement taken perpendicular to the length of beam.
Beam Length - (Measured in Meter) - Beam Length is the center to center distance between the supports or the effective length of the beam.
Elastic Modulus - (Measured in Pascal) - The Elastic Modulus is the ratio of Stress to Strain.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

STEP 1: Convert Input(s) to Base Unit

Width of Beam: 18 Millimeter --> 0.018 Meter (Check conversion here)
Beam Length: 4800 Millimeter --> 4.8 Meter (Check conversion here)
Elastic Modulus: 50 Pascal --> 50 Pascal No Conversion Required
Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (W_beam*L_beam^3)/(192*e*I) --> (0.018*4.8^3)/(192*50*1.125)

Evaluating ... ...

δ = 0.00018432

STEP 3: Convert Result to Output's Unit

0.00018432 Meter -->0.18432 Millimeter (Check conversion here)

FINAL ANSWER

0.18432 Millimeter <-- Deflection of Beam

(Calculation completed in 00.004 seconds)

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Moment of Inertia about Polar Axis

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Deflection of Fixed Beam with Load at Center Formula

Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia)
δ = (W_beam*L_beam^3)/(192*e*I)

What is Deflection?

Deflection is the degree to which a structural element is displaced under a load (due to its deformation). It may refer to an angle or a distance.

The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load.

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

Deflection of Fixed Beam with Load at Center calculator uses Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia) to calculate the Deflection of Beam, Deflection of fixed beam with load at center is giver by negative ratio of product of width of bean and cube of length to 192 times product of elastic modulus and moment of inertia. Deflection of Beam is denoted by δ symbol.

How to calculate Deflection of Fixed Beam with Load at Center using this online calculator? To use this online calculator 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. Here is how the Deflection of Fixed Beam with Load at Center calculation can be explained with given input values -> 184.32 = (0.018*4.8^3)/(192*50*1.125).

FAQ

What is Deflection of Fixed Beam with Load at Center?

Deflection of fixed beam with load at center is giver by negative ratio of product of width of bean and cube of length to 192 times product of elastic modulus and moment of inertia and is represented as δ = (W_beam*L_beam^3)/(192*e*I) or Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia). Width of Beam is the horizontal measurement taken perpendicular to the length of beam, Beam Length is the center to center distance between the supports or the effective length of the beam, The Elastic Modulus is the ratio of Stress to Strain & Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

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

Deflection of fixed beam with load at center is giver by negative ratio of product of width of bean and cube of length to 192 times product of elastic modulus and moment of inertia is calculated using Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia). To calculate Deflection of Fixed Beam with Load at Center, you need Width of Beam (W_beam), Beam Length (L_beam), Elastic Modulus (e) & Moment of Inertia (I). With our tool, you need to enter the respective value for Width of Beam, Beam Length, Elastic Modulus & Moment of Inertia and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Deflection of Beam?

In this formula, Deflection of Beam uses Width of Beam, Beam Length, Elastic Modulus & Moment of Inertia. We can use 1 other way(s) to calculate the same, which is/are as follows -

Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)

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