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Deflection of Cantilever Beam carrying Point Load at Any Point Formula

GoDeflection at Any Point on Cantilever Beam carrying UDL Formula

GoDeflection at Any Point on Cantilever Beam carrying Couple Moment at Free End Formula

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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. Check FAQs

δ = \frac{P \cdot (a^{2}) \cdot (3 \cdot l - a)}{6 \cdot E \cdot I}

δ - Deflection of Beam?P - Point Load?a - Distance from Support A?l - Length of Beam?E - Elasticity Modulus of Concrete?I - Area Moment of Inertia?

Deflection of Cantilever Beam carrying Point Load at Any Point Example

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Here is how the Deflection of Cantilever Beam carrying Point Load at Any Point equation looks like with Values.

Here is how the Deflection of Cantilever Beam carrying Point Load at Any Point equation looks like with Units.

Here is how the Deflection of Cantilever Beam carrying Point Load at Any Point equation looks like.

19.7227 = \frac{88 \cdot (2250^{2}) \cdot (3 \cdot 5000 - 2250)}{6 \cdot 30000 \cdot 0.0016}

19.7227mm = \frac{88kN \cdot ({2250mm}^{2}) \cdot (3 \cdot 5000mm - 2250mm)}{6 \cdot 30000MPa \cdot 0.0016m⁴}

19.7227 = \frac{88 \cdot (2250^{2}) \cdot (3 \cdot 5000 - 2250)}{6 \cdot 30000 \cdot 0.0016}

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Deflection of Cantilever Beam carrying Point Load at Any Point Solution

Follow our step by step solution on how to calculate Deflection of Cantilever Beam carrying Point Load at Any Point?

FIRST Step Consider the formula

δ = \frac{P \cdot (a^{2}) \cdot (3 \cdot l - a)}{6 \cdot E \cdot I}

Next Step Substitute values of Variables

∴

δ = \frac{88kN \cdot ({2250mm}^{2}) \cdot (3 \cdot 5000mm - 2250mm)}{6 \cdot 30000MPa \cdot 0.0016m⁴}

Next Step Convert Units

∴

δ = \frac{88000N \cdot ({2.25m}^{2}) \cdot (3 \cdot 5m - 2.25m)}{6 \cdot 3E+10Pa \cdot 0.0016m⁴}

Next Step Prepare to Evaluate

∴

δ = \frac{88000 \cdot ({2.25}^{2}) \cdot (3 \cdot 5 - 2.25)}{6 \cdot 3E+10 \cdot 0.0016}

Next Step Evaluate

∴

δ = 0.01972265625m

Next Step Convert to Output's Unit

∴

δ = 19.72265625mm

LAST Step Rounding Answer

∴

δ = 19.7227mm

Deflection of Cantilever Beam carrying Point Load at Any Point Formula Elements

Variables

Deflection of Beam

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.

Symbol: δ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Beam

Point Load

Point Load acting on a beam is a force applied at a single point at a set distance from the ends of the beam.

Symbol: P

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Point Load

Distance from Support A

The Distance from support A is the distance between support to point of calculation.

Symbol: a

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Support A

Length of Beam

Length of Beam is defined as the distance between the supports.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Beam

Elasticity Modulus of Concrete

Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain.

Symbol: E

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Elasticity Modulus of Concrete

Area Moment of Inertia

Area Moment of Inertia is a moment about the centroidal axis without considering mass.

Symbol: I

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Area Moment of Inertia

Other Formulas to find Deflection of Beam

Go Deflection at Any Point on Cantilever Beam carrying UDL

δ = ((w' \cdot x^{2}) \cdot (\frac{(x^{2}) + (6 \cdot l^{2}) - (4 \cdot x \cdot l)}{24 \cdot E \cdot I}))

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

δ = (\frac{M c \cdot x^{2}}{2 \cdot E \cdot I})

Go Maximum Deflection of Cantilever Beam carrying Point Load at Free End

δ = \frac{P \cdot (l^{3})}{3 \cdot E \cdot I}

Go Maximum Deflection of Cantilever Beam carrying UDL

δ = \frac{w' \cdot (l^{4})}{8 \cdot E \cdot I}

Other formulas in Cantilever Beam category

Go Slope at Free End of Cantilever Beam carrying UDL

θ = (\frac{w' \cdot l^{3}}{6 \cdot E \cdot I})

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

θ = (\frac{P \cdot x^{2}}{2 \cdot E \cdot I})

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

θ = (\frac{P \cdot l^{2}}{2 \cdot E \cdot I})

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

θ = (\frac{M c \cdot l}{E \cdot I})

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

Deflection of Cantilever Beam carrying Point Load at Any Point evaluator 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 evaluate 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 evaluate Deflection of Cantilever Beam carrying Point Load at Any Point using this online evaluator? To use this online evaluator 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.

FAQs on Deflection of Cantilever Beam carrying Point Load at Any Point

What is the formula to find Deflection of Cantilever Beam carrying Point Load at Any Point?

The formula of Deflection of Cantilever Beam carrying Point Load at Any Point is expressed as 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). Here is an example- 19722.66 = (88000*(2.25^2)*(3*5-2.25))/(6*30000000000*0.0016).

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

With Point Load (P), Distance from Support A (a), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) we can find Deflection of Cantilever Beam carrying Point Load at Any Point using the 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).

What are the other ways to Calculate Deflection of Beam?

Here are the different ways to Calculate Deflection of Beam-

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)

Can the Deflection of Cantilever Beam carrying Point Load at Any Point be negative?

No, the Deflection of Cantilever Beam carrying Point Load at Any Point, measured in Length cannot be negative.

Which unit is used to measure Deflection of Cantilever Beam carrying Point Load at Any Point?

Deflection of Cantilever Beam carrying Point Load at Any Point is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Deflection of Cantilever Beam carrying Point Load at Any Point can be measured.

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Deflection of Cantilever Beam carrying Point Load at Any Point Formula

​GoDeflection at Any Point on Cantilever Beam carrying UDL Formula

​GoDeflection at Any Point on Cantilever Beam carrying Couple Moment at Free End Formula

Deflection of Cantilever Beam carrying Point Load at Any Point Example

Deflection of Cantilever Beam carrying Point Load at Any Point Solution

Deflection of Cantilever Beam carrying Point Load at Any Point Formula Elements

Other Formulas to find Deflection of Beam

Other formulas in Cantilever Beam category

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

FAQs on Deflection of Cantilever Beam carrying Point Load at Any Point

Variable Name

GoDeflection at Any Point on Cantilever Beam carrying UDL Formula

GoDeflection at Any Point on Cantilever Beam carrying Couple Moment at Free End Formula