Deflection at Any Point on Cantilever Beam carrying UDL Calculator

✖Load per Unit Length is the load distributed per unit meter.ⓘ Load per Unit Length [w^']			+10% -10%
✖Distance x from Support is the length of a beam from the support to any point on the beam.ⓘ Distance x from Support [x]			+10% -10%
✖Length of Beam is defined as the distance between the supports.ⓘ Length of Beam [l]			+10% -10%
✖Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain.ⓘ Elasticity Modulus of Concrete [E]			+10% -10%
✖Area Moment of Inertia is a moment about the centroidal axis without considering mass.ⓘ Area Moment of Inertia [I]			+10% -10%

✖Deflection of Beam Deflection is the movement of a beam or node from its original position. It happens due to the forces and loads being applied to the body.ⓘ Deflection at Any Point on Cantilever Beam carrying UDL [δ]

⎘ Copy

👎

Formula

✖

Deflection at Any Point on Cantilever Beam carrying UDL

Formula

`"δ" = (("w"^{"'"}*"x"^2)*((("x"^2)+(6*"l"^2)-(4*"x"*"l"))/(24*"E"*"I")))`

Example

`"4.425335mm"=(("24kN/m"*("1300mm")^2)*(((("1300mm")^2)+(6*("5000mm")^2)-(4*"1300mm"*"5000mm"))/(24*"30000MPa"*"0.0016m⁴")))`

Calculator

LaTeX

Reset

👍

Download Slope and Deflection Formulas PDF

Deflection at Any Point on Cantilever Beam carrying UDL Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)-(4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia)))
δ = ((w^'*x^2)*(((x^2)+(6*l^2)-(4*x*l))/(24*E*I)))
This formula uses 6 Variables

Variables Used

Deflection of Beam - (Measured in Meter) - Deflection of Beam Deflection is the movement of a beam or node from its original position. It happens due to the forces and loads being applied to the body.
Load per Unit Length - (Measured in Newton per Meter) - Load per Unit Length is the load distributed per unit meter.
Distance x from Support - (Measured in Meter) - Distance x from Support is the length of a beam from the support to any point on the beam.
Length of Beam - (Measured in Meter) - Length of Beam is defined as the distance between the supports.
Elasticity Modulus of Concrete - (Measured in Pascal) - Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain.
Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a moment about the centroidal axis without considering mass.

STEP 1: Convert Input(s) to Base Unit

Load per Unit Length: 24 Kilonewton per Meter --> 24000 Newton per Meter (Check conversion here)
Distance x from Support: 1300 Millimeter --> 1.3 Meter (Check conversion here)
Length of Beam: 5000 Millimeter --> 5 Meter (Check conversion here)
Elasticity Modulus of Concrete: 30000 Megapascal --> 30000000000 Pascal (Check conversion here)
Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = ((w^'*x^2)*(((x^2)+(6*l^2)-(4*x*l))/(24*E*I))) --> ((24000*1.3^2)*(((1.3^2)+(6*5^2)-(4*1.3*5))/(24*30000000000*0.0016)))

Evaluating ... ...

δ = 0.00442533541666667

STEP 3: Convert Result to Output's Unit

0.00442533541666667 Meter -->4.42533541666667 Millimeter (Check conversion here)

FINAL ANSWER

4.42533541666667 ≈ 4.425335 Millimeter <-- Deflection of Beam

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Strength of Materials » Slope and Deflection » Cantilever Beam » Deflection at Any Point on Cantilever Beam carrying UDL

Credits

Created by krupa sheela pattapu

Acharya Nagarjuna University College of Engg & Technology (ANU), Guntur

krupa sheela pattapu has created this Calculator and 25+ more calculators!

Verified by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has verified this Calculator and 700+ more calculators!

< 13 Cantilever Beam Calculators

Deflection at Any Point on Cantilever Beam carrying UDL

Go Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)-(4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia)))

Deflection of Cantilever Beam carrying Point Load at Any Point

Go Deflection of Beam = (Point Load*(Distance from Support A^2)*(3*Length of Beam-Distance from Support A))/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)

Maximum Deflection of Cantilever Beam Carrying UVL with Maximum Intensity at Free End

Go Deflection of Beam = ((11*Uniformly Varying Load*(Length of Beam^4))/(120*Elasticity Modulus of Concrete*Area Moment of Inertia))

Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End

Go Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))

Maximum Deflection of Cantilever Beam carrying UVL with Maximum Intensity at Support

Go Deflection of Beam = (Uniformly Varying Load*(Length of Beam^4))/(30*Elasticity Modulus of Concrete*Area Moment of Inertia)

Maximum Deflection of Cantilever Beam carrying UDL

Go Deflection of Beam = (Load per Unit Length*(Length of Beam^4))/(8*Elasticity Modulus of Concrete*Area Moment of Inertia)

Slope at Free End of Cantilever Beam Carrying UVL with Maximum Intensity at Fixed End

Go Slope of Beam = ((Uniformly Varying Load*Length of Beam^3)/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))

Maximum Deflection of Cantilever Beam with Couple Moment at Free End

Go Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia)

Slope at Free End of Cantilever Beam carrying UDL

Go Slope of Beam = ((Load per Unit Length*Length of Beam^3)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia))

Slope at Free End of Cantilever Beam Carrying Concentrated Load at Any Point from Fixed End

Go Slope of Beam = ((Point Load*Distance x from Support^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))

Maximum Deflection of Cantilever Beam carrying Point Load at Free End

Go Deflection of Beam = (Point Load*(Length of Beam^3))/(3*Elasticity Modulus of Concrete*Area Moment of Inertia)

Slope at Free End of Cantilever Beam Carrying Couple at Free End

Go Slope of Beam = ((Moment of Couple*Length of Beam)/(Elasticity Modulus of Concrete*Area Moment of Inertia))

Slope at Free End of Cantilever Beam Carrying Concentrated Load at Free End

Go Slope of Beam = ((Point Load*Length of Beam^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))

Deflection at Any Point on Cantilever Beam carrying UDL Formula

What is Beam Deflection?

The Deformation of a Beam is usually expressed in terms of its deflection from its original unloaded position. The deflection is measured from the original neutral surface of the beam to the neutral surface of the deformed beam. The configuration assumed by the deformed neutral surface is known as the elastic curve of the beam.

What is UDL?

The uniformly distributed load (UDL) is a load that is distributed or spread across the whole region of an element such as a beam or slab. In other words, the magnitude of the load remains uniform throughout the whole element.

How to Calculate Deflection at Any Point on Cantilever Beam carrying UDL?

Deflection at Any Point on Cantilever Beam carrying UDL calculator uses Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)-(4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))) to calculate the Deflection of Beam, The Deflection at Any Point on Cantilever Beam carrying UDL formula is defined as the distance between its position before and after loading. Deflection of Beam is denoted by δ symbol.

How to calculate Deflection at Any Point on Cantilever Beam carrying UDL using this online calculator? To use this online calculator for Deflection at Any Point on Cantilever Beam carrying UDL, enter Load per Unit Length (w^'), Distance x from Support (x), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) and hit the calculate button. Here is how the Deflection at Any Point on Cantilever Beam carrying UDL calculation can be explained with given input values -> 4425.335 = ((24000*1.3^2)*(((1.3^2)+(6*5^2)-(4*1.3*5))/(24*30000000000*0.0016))).

FAQ

What is Deflection at Any Point on Cantilever Beam carrying UDL?

The Deflection at Any Point on Cantilever Beam carrying UDL formula is defined as the distance between its position before and after loading and is represented as δ = ((w^'*x^2)*(((x^2)+(6*l^2)-(4*x*l))/(24*E*I))) or Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)-(4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))). Load per Unit Length is the load distributed per unit meter, Distance x from Support is the length of a beam from the support to any point on the beam, Length of Beam is defined as the distance between the supports, Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain & Area Moment of Inertia is a moment about the centroidal axis without considering mass.

How to calculate Deflection at Any Point on Cantilever Beam carrying UDL?

The Deflection at Any Point on Cantilever Beam carrying UDL formula is defined as the distance between its position before and after loading is calculated using Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)-(4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))). To calculate Deflection at Any Point on Cantilever Beam carrying UDL, you need Load per Unit Length (w^'), Distance x from Support (x), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I). With our tool, you need to enter the respective value for Load per Unit Length, Distance x from Support, Length of Beam, Elasticity Modulus of Concrete & Area 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 Load per Unit Length, Distance x from Support, Length of Beam, Elasticity Modulus of Concrete & Area Moment of Inertia. We can use 7 other way(s) to calculate the same, which is/are as follows -

Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))
Deflection of Beam = (Point Load*(Distance from Support A^2)*(3*Length of Beam-Distance from Support A))/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = (Point Load*(Length of Beam^3))/(3*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = (Load per Unit Length*(Length of Beam^4))/(8*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = (Uniformly Varying Load*(Length of Beam^4))/(30*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = ((11*Uniformly Varying Load*(Length of Beam^4))/(120*Elasticity Modulus of Concrete*Area Moment of Inertia))
Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia)

Home

FREE PDFs

🔍 Search