Deflection of Cantilever Beam carrying Point Load at Any Point Calculator

✖Point Load acting on a beam is a force applied at a single point at a set distance from the ends of the beam.ⓘ Point Load [P]			+10% -10%
✖The Distance from support A is the distance between support to point of calculation.ⓘ Distance from Support A [a]			+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 of Cantilever Beam carrying Point Load at Any Point [δ]

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Deflection of Cantilever Beam carrying Point Load at Any Point

Formula

`"δ" = ("P"*("a"^2)*(3*"l"-"a"))/(6*"E"*"I")`

Example

`"19.72266mm"=("88kN"*(("2250mm")^2)*(3*"5000mm"-"2250mm"))/(6*"30000MPa"*"0.0016m⁴")`

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Deflection of Cantilever Beam carrying Point Load at Any Point Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
δ = (P*(a^2)*(3*l-a))/(6*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.
Point Load - (Measured in Newton) - Point Load acting on a beam is a force applied at a single point at a set distance from the ends of the beam.
Distance from Support A - (Measured in Meter) - The Distance from support A is the distance between support to point of calculation.
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

Point Load: 88 Kilonewton --> 88000 Newton (Check conversion here)
Distance from Support A: 2250 Millimeter --> 2.25 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 = (P*(a^2)*(3*l-a))/(6*E*I) --> (88000*(2.25^2)*(3*5-2.25))/(6*30000000000*0.0016)

Evaluating ... ...

δ = 0.01972265625

STEP 3: Convert Result to Output's Unit

0.01972265625 Meter -->19.72265625 Millimeter (Check conversion here)

FINAL ANSWER

19.72265625 ≈ 19.72266 Millimeter <-- Deflection of Beam

(Calculation completed in 00.004 seconds)

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

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< 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 of Cantilever Beam carrying Point Load at Any Point Formula

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)
δ = (P*(a^2)*(3*l-a))/(6*E*I)

What is Maximum and Center Deflection of Cantilever Beam carrying Point Load at any point?

The Maximum and Center Deflection of Cantilever Beam carrying Point Load at any point is the maximum degree to which a Cantilever beam is displaced under a Point load.

How to Calculate Deflection of Cantilever Beam carrying Point Load at Any Point?

Deflection of Cantilever Beam carrying Point Load at Any Point calculator uses 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) to calculate the Deflection of Beam, The Deflection of Cantilever Beam carrying Point Load at Any Point formula is defined as (Point Load acting on Beam*(Distance From End A^2)*(3*Length of the Beam - Distance from end A))/(6*Modulus of Elasticity*Area Moment of Inertia). Deflection of Beam is denoted by δ symbol.

How to calculate Deflection of Cantilever Beam carrying Point Load at Any Point using this online calculator? To use this online calculator for Deflection of Cantilever Beam carrying Point Load at Any Point, enter Point Load (P), Distance from Support A (a), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) and hit the calculate button. Here is how the Deflection of Cantilever Beam carrying Point Load at Any Point calculation can be explained with given input values -> 19722.66 = (88000*(2.25^2)*(3*5-2.25))/(6*30000000000*0.0016).

FAQ

What is Deflection of Cantilever Beam carrying Point Load at Any Point?

The Deflection of Cantilever Beam carrying Point Load at Any Point formula is defined as (Point Load acting on Beam*(Distance From End A^2)*(3*Length of the Beam - Distance from end A))/(6*Modulus of Elasticity*Area Moment of Inertia) and is represented as δ = (P*(a^2)*(3*l-a))/(6*E*I) or 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). Point Load acting on a beam is a force applied at a single point at a set distance from the ends of the beam, The Distance from support A is the distance between support to point of calculation, 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 of Cantilever Beam carrying Point Load at Any Point?

The Deflection of Cantilever Beam carrying Point Load at Any Point formula is defined as (Point Load acting on Beam*(Distance From End A^2)*(3*Length of the Beam - Distance from end A))/(6*Modulus of Elasticity*Area Moment of Inertia) is calculated using 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). To calculate Deflection of Cantilever Beam carrying Point Load at Any Point, you need Point Load (P), Distance from Support A (a), 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 Point Load, Distance from Support A, 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 Point Load, Distance from Support A, 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 = ((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 Beam = ((Moment of Couple*Distance x from Support^2)/(2*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)

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