Deflection of Fixed Beam with Uniformly Distributed Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)
δ = (Wbeam*Lbeam^4)/(384*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 = (Wbeam*Lbeam^4)/(384*e*I) --> (0.018*4.8^4)/(384*50*1.125)
Evaluating ... ...
δ = 0.000442368
STEP 3: Convert Result to Output's Unit
0.000442368 Meter -->0.442368 Millimeter (Check conversion here)
FINAL ANSWER
0.442368 Millimeter <-- Deflection of Beam
(Calculation completed in 00.004 seconds)

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7 Stress and Strain Calculators

Elongation Circular Tapered Bar
Go Elongation = (4*Load*Length of Bar)/(pi*Diameter of Bigger End*Diameter of Smaller End*Elastic Modulus)
Moment of Inertia for Hollow Circular Shaft
Go Polar Moment of Inertia = pi/32*(Outer Diameter of Hollow Circular Section^(4)-Inner Diameter of Hollow Circular Section^(4))
Deflection of Fixed Beam with Uniformly Distributed Load
Go Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)
Deflection of Fixed Beam with Load at Center
Go Deflection of Beam = (Width of Beam*Beam Length^3)/(192*Elastic Modulus*Moment of Inertia)
Elongation of Prismatic Bar due to its Own Weight
Go Elongation = (2*Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)
Axial Elongation of Prismatic Bar due to External Load
Go Elongation = (Load*Length of Bar)/(Area of Prismatic Bar*Elastic Modulus)
Moment of Inertia about Polar Axis
Go Polar Moment of Inertia = (pi*Diameter of Shaft^(4))/32

Deflection of Fixed Beam with Uniformly Distributed Load Formula

Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia)
δ = (Wbeam*Lbeam^4)/(384*e*I)

What is deflection?

Deflection is the degree to which a structural element is displaced under a load (due to its deformation). The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory.

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

Deflection of Fixed Beam with Uniformly Distributed Load calculator uses Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia) to calculate the Deflection of Beam, The deflection of fixed beam with uniformly distributed load is ratio of product of width and fourth power of length to 384 times the product of elastic modulus and moment of inertia. Deflection of Beam is denoted by δ symbol.

How to calculate Deflection of Fixed Beam with Uniformly Distributed Load using this online calculator? To use this online calculator for Deflection of Fixed Beam with Uniformly Distributed Load, enter Width of Beam (Wbeam), Beam Length (Lbeam), Elastic Modulus (e) & Moment of Inertia (I) and hit the calculate button. Here is how the Deflection of Fixed Beam with Uniformly Distributed Load calculation can be explained with given input values -> 442.368 = (0.018*4.8^4)/(384*50*1.125).

FAQ

What is Deflection of Fixed Beam with Uniformly Distributed Load?
The deflection of fixed beam with uniformly distributed load is ratio of product of width and fourth power of length to 384 times the product of elastic modulus and moment of inertia and is represented as δ = (Wbeam*Lbeam^4)/(384*e*I) or Deflection of Beam = (Width of Beam*Beam Length^4)/(384*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 Uniformly Distributed Load?
The deflection of fixed beam with uniformly distributed load is ratio of product of width and fourth power of length to 384 times the product of elastic modulus and moment of inertia is calculated using Deflection of Beam = (Width of Beam*Beam Length^4)/(384*Elastic Modulus*Moment of Inertia). To calculate Deflection of Fixed Beam with Uniformly Distributed Load, you need Width of Beam (Wbeam), Beam Length (Lbeam), 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^3)/(192*Elastic Modulus*Moment of Inertia)
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