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Slope at Free End of Cantilever Beam carrying UDL Formula

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

GoSlope at Free End of Cantilever Beam Carrying Concentrated Load at Free End Formula

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The Slope of Beam is the angle between deflected beam to the actual beam at the same point. Check FAQs

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

θ - Slope of Beam?w^' - Load per Unit Length?l - Length of Beam?E - Elasticity Modulus of Concrete?I - Area Moment of Inertia?

Slope at Free End of Cantilever Beam carrying UDL Example

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Here is how the Slope at Free End of Cantilever Beam carrying UDL equation looks like with Values.

Here is how the Slope at Free End of Cantilever Beam carrying UDL equation looks like with Units.

Here is how the Slope at Free End of Cantilever Beam carrying UDL equation looks like.

0.0104 = (\frac{24 \cdot 5000^{3}}{6 \cdot 30000 \cdot 0.0016})

0.0104rad = (\frac{24kN/m \cdot {5000mm}^{3}}{6 \cdot 30000MPa \cdot 0.0016m⁴})

0.0104 = (\frac{24 \cdot 5000^{3}}{6 \cdot 30000 \cdot 0.0016})

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Slope at Free End of Cantilever Beam carrying UDL Solution

Follow our step by step solution on how to calculate Slope at Free End of Cantilever Beam carrying UDL?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ = (\frac{24kN/m \cdot {5000mm}^{3}}{6 \cdot 30000MPa \cdot 0.0016m⁴})

Next Step Convert Units

∴

θ = (\frac{24000N/m \cdot {5m}^{3}}{6 \cdot 3E+10Pa \cdot 0.0016m⁴})

Next Step Prepare to Evaluate

∴

θ = (\frac{24000 \cdot 5^{3}}{6 \cdot 3E+10 \cdot 0.0016})

Next Step Evaluate

∴

θ = 0.0104166666666667rad

LAST Step Rounding Answer

∴

θ = 0.0104rad

Slope at Free End of Cantilever Beam carrying UDL Formula Elements

Variables

Slope of Beam

The Slope of Beam is the angle between deflected beam to the actual beam at the same point.

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Slope 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

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 Slope of Beam

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})

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

θ = (\frac{q \cdot l^{3}}{24 \cdot E \cdot I})

Other formulas in Cantilever Beam category

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}

How to Evaluate Slope at Free End of Cantilever Beam carrying UDL?

Slope at Free End of Cantilever Beam carrying UDL evaluator uses Slope of Beam = ((Load per Unit Length*Length of Beam^3)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)) to evaluate the Slope of Beam, The Slope at Free End of Cantilever Beam carrying UDL formula is defined as angle between deflected beam to the actual beam at the same point. Slope of Beam is denoted by θ symbol.

How to evaluate Slope at Free End of Cantilever Beam carrying UDL using this online evaluator? To use this online evaluator for Slope at Free End of Cantilever Beam carrying UDL, enter Load per Unit Length (w^'), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) and hit the calculate button.

FAQs on Slope at Free End of Cantilever Beam carrying UDL

What is the formula to find Slope at Free End of Cantilever Beam carrying UDL?

The formula of Slope at Free End of Cantilever Beam carrying UDL is expressed as Slope of Beam = ((Load per Unit Length*Length of Beam^3)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)). Here is an example- 0.010417 = ((24000*5^3)/(6*30000000000*0.0016)).

How to calculate Slope at Free End of Cantilever Beam carrying UDL?

With Load per Unit Length (w^'), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) we can find Slope at Free End of Cantilever Beam carrying UDL using the formula - Slope of Beam = ((Load per Unit Length*Length of Beam^3)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)).

What are the other ways to Calculate Slope of Beam?

Here are the different ways to Calculate Slope of Beam-

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

Can the Slope at Free End of Cantilever Beam carrying UDL be negative?

No, the Slope at Free End of Cantilever Beam carrying UDL, measured in Angle cannot be negative.

Which unit is used to measure Slope at Free End of Cantilever Beam carrying UDL?

Slope at Free End of Cantilever Beam carrying UDL is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Slope at Free End of Cantilever Beam carrying UDL can be measured.

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Slope at Free End of Cantilever Beam carrying UDL Formula

​GoSlope at Free End of Cantilever Beam Carrying Concentrated Load at Any Point from Fixed End Formula

​GoSlope at Free End of Cantilever Beam Carrying Concentrated Load at Free End Formula

Slope at Free End of Cantilever Beam carrying UDL Example

Slope at Free End of Cantilever Beam carrying UDL Solution

Slope at Free End of Cantilever Beam carrying UDL Formula Elements

Other Formulas to find Slope of Beam

Other formulas in Cantilever Beam category

How to Evaluate Slope at Free End of Cantilever Beam carrying UDL?

FAQs on Slope at Free End of Cantilever Beam carrying UDL

Variable Name

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

GoSlope at Free End of Cantilever Beam Carrying Concentrated Load at Free End Formula