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Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center Formula

GoSlope at Free Ends of Simply Supported Beam carrying UDL Formula

GoSlope at Left End of Simply Supported Beam carrying Couple at Right 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{P \cdot l^{2}}{16 \cdot E \cdot I})

θ - Slope of Beam?P - Point Load?l - Length of Beam?E - Elasticity Modulus of Concrete?I - Area Moment of Inertia?

Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center Example

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Here is how the Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center equation looks like with Values.

Here is how the Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center equation looks like with Units.

Here is how the Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center equation looks like.

0.0029 = (\frac{88 \cdot 5000^{2}}{16 \cdot 30000 \cdot 0.0016})

0.0029rad = (\frac{88kN \cdot {5000mm}^{2}}{16 \cdot 30000MPa \cdot 0.0016m⁴})

0.0029 = (\frac{88 \cdot 5000^{2}}{16 \cdot 30000 \cdot 0.0016})

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Strength of Materials » fx Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center

Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center Solution

Follow our step by step solution on how to calculate Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center?

FIRST Step Consider the formula

θ = (\frac{P \cdot l^{2}}{16 \cdot E \cdot I})

Next Step Substitute values of Variables

∴

θ = (\frac{88kN \cdot {5000mm}^{2}}{16 \cdot 30000MPa \cdot 0.0016m⁴})

Next Step Convert Units

∴

θ = (\frac{88000N \cdot {5m}^{2}}{16 \cdot 3E+10Pa \cdot 0.0016m⁴})

Next Step Prepare to Evaluate

∴

θ = (\frac{88000 \cdot 5^{2}}{16 \cdot 3E+10 \cdot 0.0016})

Next Step Evaluate

∴

θ = 0.00286458333333333rad

LAST Step Rounding Answer

∴

θ = 0.0029rad

Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center 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

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

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 Ends of Simply Supported Beam carrying UDL

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

Go Slope at Left End of Simply Supported Beam carrying Couple at Right End

θ = (\frac{M c \cdot l}{6 \cdot E \cdot I})

Go Slope at Left End of Simply Supported Beam carrying UVL with Maximum Intensity at Right End

θ = (\frac{7 \cdot q \cdot l^{3}}{360 \cdot E \cdot I})

Go Slope at Right End of Simply Supported Beam carrying Couple at Right End

θ = (\frac{M c \cdot l}{3 \cdot E \cdot I})

Other formulas in Simply Supported Beam category

Go Center Deflection of Simply Supported Beam carrying Couple Moment at Right End

δ = (\frac{M c \cdot l^{2}}{16 \cdot E \cdot I})

Go Center Deflection on Simply Supported Beam carrying UVL with Maximum Intensity at Right support

δ = (0.00651 \cdot \frac{q \cdot (l^{4})}{E \cdot I})

Go Deflection at Any Point on Simply Supported carrying Couple Moment at Right End

δ = ((\frac{M c \cdot l \cdot x}{6 \cdot E \cdot I}) \cdot (1 - (\frac{x^{2}}{l^{2}})))

Go Deflection at Any Point on Simply Supported Beam carrying UDL

δ = (((\frac{w' \cdot x}{24 \cdot E \cdot I}) \cdot ((l^{3}) - (2 \cdot l \cdot x^{2}) + (x^{3}))))

How to Evaluate Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center?

Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center evaluator uses Slope of Beam = ((Point Load*Length of Beam^2)/(16*Elasticity Modulus of Concrete*Area Moment of Inertia)) to evaluate the Slope of Beam, The Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center 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 Ends of Simply Supported Beam carrying Concentrated Load at Center using this online evaluator? To use this online evaluator for Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center, enter Point Load (P), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) and hit the calculate button.

FAQs on Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center

What is the formula to find Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center?

The formula of Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center is expressed as Slope of Beam = ((Point Load*Length of Beam^2)/(16*Elasticity Modulus of Concrete*Area Moment of Inertia)). Here is an example- 0.002865 = ((88000*5^2)/(16*30000000000*0.0016)).

How to calculate Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center?

With Point Load (P), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) we can find Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center using the formula - Slope of Beam = ((Point Load*Length of Beam^2)/(16*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=((Load per Unit Length*Length of Beam^3)/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))
Slope of Beam=((Moment of Couple*Length of Beam)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia))
Slope of Beam=((7*Uniformly Varying Load*Length of Beam^3)/(360*Elasticity Modulus of Concrete*Area Moment of Inertia))

Can the Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center be negative?

No, the Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center, measured in Angle cannot be negative.

Which unit is used to measure Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center?

Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center 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 Ends of Simply Supported Beam carrying Concentrated Load at Center can be measured.

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Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center Formula

​GoSlope at Free Ends of Simply Supported Beam carrying UDL Formula

​GoSlope at Left End of Simply Supported Beam carrying Couple at Right End Formula

Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center Example

Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center Solution

Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center Formula Elements

Other Formulas to find Slope of Beam

Other formulas in Simply Supported Beam category

How to Evaluate Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center?

FAQs on Slope at Free Ends of Simply Supported Beam carrying Concentrated Load at Center

Variable Name

GoSlope at Free Ends of Simply Supported Beam carrying UDL Formula

GoSlope at Left End of Simply Supported Beam carrying Couple at Right End Formula