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Deflection at Any Point on Cantilever Beam carrying UDL Formula

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

GoDeflection of Cantilever Beam carrying Point Load at Any Point 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 = ((w' \cdot x^{2}) \cdot (\frac{(x^{2}) + (6 \cdot l^{2}) - (4 \cdot x \cdot l)}{24 \cdot E \cdot I}))

δ - Deflection of Beam?w^' - Load per Unit Length?x - Distance x from Support?l - Length of Beam?E - Elasticity Modulus of Concrete?I - Area Moment of Inertia?

Deflection at Any Point on Cantilever Beam carrying UDL Example

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

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

Here is how the Deflection at Any Point on Cantilever Beam carrying UDL equation looks like.

4.4253 = ((24 \cdot 1300^{2}) \cdot (\frac{(1300^{2}) + (6 \cdot 5000^{2}) - (4 \cdot 1300 \cdot 5000)}{24 \cdot 30000 \cdot 0.0016}))

4.4253mm = ((24kN/m \cdot {1300mm}^{2}) \cdot (\frac{({1300mm}^{2}) + (6 \cdot {5000mm}^{2}) - (4 \cdot 1300mm \cdot 5000mm)}{24 \cdot 30000MPa \cdot 0.0016m⁴}))

4.4253 = ((24 \cdot 1300^{2}) \cdot (\frac{(1300^{2}) + (6 \cdot 5000^{2}) - (4 \cdot 1300 \cdot 5000)}{24 \cdot 30000 \cdot 0.0016}))

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Deflection at Any Point on Cantilever Beam carrying UDL Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ = ((24kN/m \cdot {1300mm}^{2}) \cdot (\frac{({1300mm}^{2}) + (6 \cdot {5000mm}^{2}) - (4 \cdot 1300mm \cdot 5000mm)}{24 \cdot 30000MPa \cdot 0.0016m⁴}))

Next Step Convert Units

∴

δ = ((24000N/m \cdot {1.3m}^{2}) \cdot (\frac{({1.3m}^{2}) + (6 \cdot {5m}^{2}) - (4 \cdot 1.3m \cdot 5m)}{24 \cdot 3E+10Pa \cdot 0.0016m⁴}))

Next Step Prepare to Evaluate

∴

δ = ((24000 \cdot {1.3}^{2}) \cdot (\frac{({1.3}^{2}) + (6 \cdot 5^{2}) - (4 \cdot 1.3 \cdot 5)}{24 \cdot 3E+10 \cdot 0.0016}))

Next Step Evaluate

∴

δ = 0.00442533541666667m

Next Step Convert to Output's Unit

∴

δ = 4.42533541666667mm

LAST Step Rounding Answer

∴

δ = 4.4253mm

Deflection at Any Point on Cantilever Beam carrying UDL 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

Load per Unit Length

Load per Unit Length is the load distributed per unit meter.

Symbol: w^'

Measurement: Surface TensionUnit: kN/m

Note: Value can be positive or negative.

Formulas to find Load per Unit Length

Distance x from Support

Distance x from Support is the length of a beam from the support to any point on the beam.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance x from Support

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 Couple Moment at Free End

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

Go Deflection of Cantilever Beam carrying Point Load at Any Point

δ = \frac{P \cdot (a^{2}) \cdot (3 \cdot l - a)}{6 \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 at Any Point on Cantilever Beam carrying UDL?

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

FAQs on Deflection at Any Point on Cantilever Beam carrying UDL

What is the formula to find Deflection at Any Point on Cantilever Beam carrying UDL?

The formula of Deflection at Any Point on Cantilever Beam carrying UDL is expressed as 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))). Here is an example- 4425.335 = ((24000*1.3^2)*(((1.3^2)+(6*5^2)-(4*1.3*5))/(24*30000000000*0.0016))).

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

With Load per Unit Length (w^'), Distance x from Support (x), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) we can find Deflection at Any Point on Cantilever Beam carrying UDL using the formula - 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))).

What are the other ways to Calculate Deflection of Beam?

Here are the different ways to Calculate Deflection of Beam-

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)

Can the Deflection at Any Point on Cantilever Beam carrying UDL be negative?

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

Which unit is used to measure Deflection at Any Point on Cantilever Beam carrying UDL?

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

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Deflection at Any Point on Cantilever Beam carrying UDL Formula

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

​GoDeflection of Cantilever Beam carrying Point Load at Any Point Formula

Deflection at Any Point on Cantilever Beam carrying UDL Example

Deflection at Any Point on Cantilever Beam carrying UDL Solution

Deflection at Any Point on Cantilever Beam carrying UDL Formula Elements

Other Formulas to find Deflection of Beam

Other formulas in Cantilever Beam category

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

FAQs on Deflection at Any Point on Cantilever Beam carrying UDL

Variable Name

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

GoDeflection of Cantilever Beam carrying Point Load at Any Point Formula