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Maximum Deflection of Cantilever Beam with Couple Moment at Free End 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{M c \cdot (l^{2})}{2 \cdot E \cdot I}

δ - Deflection of Beam?M_c - Moment of Couple?l - Length of Beam?E - Elasticity Modulus of Concrete?I - Area Moment of Inertia?

Maximum Deflection of Cantilever Beam with Couple Moment at Free End Example

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Here is how the Maximum Deflection of Cantilever Beam with Couple Moment at Free End equation looks like with Values.

Here is how the Maximum Deflection of Cantilever Beam with Couple Moment at Free End equation looks like with Units.

Here is how the Maximum Deflection of Cantilever Beam with Couple Moment at Free End equation looks like.

22.1354 = \frac{85 \cdot (5000^{2})}{2 \cdot 30000 \cdot 0.0016}

22.1354mm = \frac{85kN*m \cdot ({5000mm}^{2})}{2 \cdot 30000MPa \cdot 0.0016m⁴}

22.1354 = \frac{85 \cdot (5000^{2})}{2 \cdot 30000 \cdot 0.0016}

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Maximum Deflection of Cantilever Beam with Couple Moment at Free End Solution

Follow our step by step solution on how to calculate Maximum Deflection of Cantilever Beam with Couple Moment at Free End?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ = \frac{85kN*m \cdot ({5000mm}^{2})}{2 \cdot 30000MPa \cdot 0.0016m⁴}

Next Step Convert Units

∴

δ = \frac{85000N*m \cdot ({5m}^{2})}{2 \cdot 3E+10Pa \cdot 0.0016m⁴}

Next Step Prepare to Evaluate

∴

δ = \frac{85000 \cdot (5^{2})}{2 \cdot 3E+10 \cdot 0.0016}

Next Step Evaluate

∴

δ = 0.0221354166666667m

Next Step Convert to Output's Unit

∴

δ = 22.1354166666667mm

LAST Step Rounding Answer

∴

δ = 22.1354mm

Maximum Deflection of Cantilever Beam with Couple Moment at Free End 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

Moment of Couple

Moment of couple is equal to the product of either of forces and the perpendicular distance between the forces.

Symbol: M_c

Measurement: Moment of ForceUnit: kN*m

Note: Value can be positive or negative.

Formulas to find Moment of Couple

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 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}

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 Maximum Deflection of Cantilever Beam with Couple Moment at Free End?

Maximum Deflection of Cantilever Beam with Couple Moment at Free End evaluator uses Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia) to evaluate the Deflection of Beam, The Maximum Deflection of Cantilever Beam with Couple Moment at Free End formula is defined as (Couple Moment*(length of the beam^2))/(2*Modulus of Elasticity*Area Moment of inertia). Deflection of Beam is denoted by δ symbol.

How to evaluate Maximum Deflection of Cantilever Beam with Couple Moment at Free End using this online evaluator? To use this online evaluator for Maximum Deflection of Cantilever Beam with Couple Moment at Free End, enter Moment of Couple (M_c), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) and hit the calculate button.

FAQs on Maximum Deflection of Cantilever Beam with Couple Moment at Free End

What is the formula to find Maximum Deflection of Cantilever Beam with Couple Moment at Free End?

The formula of Maximum Deflection of Cantilever Beam with Couple Moment at Free End is expressed as Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia). Here is an example- 22135.42 = (85000*(5^2))/(2*30000000000*0.0016).

How to calculate Maximum Deflection of Cantilever Beam with Couple Moment at Free End?

With Moment of Couple (M_c), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) we can find Maximum Deflection of Cantilever Beam with Couple Moment at Free End using the formula - Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*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*(Distance from Support A^2)*(3*Length of Beam-Distance from Support A))/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)

Can the Maximum Deflection of Cantilever Beam with Couple Moment at Free End be negative?

No, the Maximum Deflection of Cantilever Beam with Couple Moment at Free End, measured in Length cannot be negative.

Which unit is used to measure Maximum Deflection of Cantilever Beam with Couple Moment at Free End?

Maximum Deflection of Cantilever Beam with Couple Moment at Free End is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Maximum Deflection of Cantilever Beam with Couple Moment at Free End can be measured.

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Maximum Deflection of Cantilever Beam with Couple Moment at Free End 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

Maximum Deflection of Cantilever Beam with Couple Moment at Free End Example

Maximum Deflection of Cantilever Beam with Couple Moment at Free End Solution

Maximum Deflection of Cantilever Beam with Couple Moment at Free End Formula Elements

Other Formulas to find Deflection of Beam

Other formulas in Cantilever Beam category

How to Evaluate Maximum Deflection of Cantilever Beam with Couple Moment at Free End?

FAQs on Maximum Deflection of Cantilever Beam with Couple Moment at Free End

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