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Deflection at Any Point on Simply Supported Beam carrying UDL Formula

GoCenter Deflection of Simply Supported Beam carrying Couple Moment at Right End Formula

GoCenter Deflection on Simply Supported Beam carrying UVL with Maximum Intensity at Right support 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{w' \cdot x}{24 \cdot E \cdot I}) \cdot ((l^{3}) - (2 \cdot l \cdot x^{2}) + (x^{3}))))

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

Deflection at Any Point on Simply Supported Beam carrying UDL Example

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

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

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

2.9872 = (((\frac{24 \cdot 1300}{24 \cdot 30000 \cdot 0.0016}) \cdot ((5000^{3}) - (2 \cdot 5000 \cdot 1300^{2}) + (1300^{3}))))

2.9872mm = (((\frac{24kN/m \cdot 1300mm}{24 \cdot 30000MPa \cdot 0.0016m⁴}) \cdot (({5000mm}^{3}) - (2 \cdot 5000mm \cdot {1300mm}^{2}) + ({1300mm}^{3}))))

2.9872 = (((\frac{24 \cdot 1300}{24 \cdot 30000 \cdot 0.0016}) \cdot ((5000^{3}) - (2 \cdot 5000 \cdot 1300^{2}) + (1300^{3}))))

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Strength of Materials » fx Deflection at Any Point on Simply Supported Beam carrying UDL

Deflection at Any Point on Simply Supported Beam carrying UDL Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

δ = (((\frac{24kN/m \cdot 1300mm}{24 \cdot 30000MPa \cdot 0.0016m⁴}) \cdot (({5000mm}^{3}) - (2 \cdot 5000mm \cdot {1300mm}^{2}) + ({1300mm}^{3}))))

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

δ = 0.00298721041666667m

Next Step Convert to Output's Unit

∴

δ = 2.98721041666667mm

LAST Step Rounding Answer

∴

δ = 2.9872mm

Deflection at Any Point on Simply Supported 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

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

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

Other Formulas to find Deflection of Beam

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 Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center

δ = \frac{P \cdot (l^{3})}{48 \cdot E \cdot I}

Other formulas in Simply Supported Beam category

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 Free Ends of Simply Supported Beam carrying Concentrated Load at Center

θ = (\frac{P \cdot l^{2}}{16 \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})

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

Deflection at Any Point on Simply Supported Beam carrying UDL evaluator uses Deflection of Beam = ((((Load per Unit Length*Distance x from Support)/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))*((Length of Beam^3)-(2*Length of Beam*Distance x from Support^2)+(Distance x from Support^3)))) to evaluate the Deflection of Beam, The Deflection at Any Point on Simply Supported 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 Simply Supported Beam carrying UDL using this online evaluator? To use this online evaluator for Deflection at Any Point on Simply Supported Beam carrying UDL, enter Load per Unit Length (w^'), Distance x from Support (x), Elasticity Modulus of Concrete (E), Area Moment of Inertia (I) & Length of Beam (l) and hit the calculate button.

FAQs on Deflection at Any Point on Simply Supported Beam carrying UDL

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

The formula of Deflection at Any Point on Simply Supported Beam carrying UDL is expressed as Deflection of Beam = ((((Load per Unit Length*Distance x from Support)/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))*((Length of Beam^3)-(2*Length of Beam*Distance x from Support^2)+(Distance x from Support^3)))). Here is an example- 2987.21 = ((((24000*1.3)/(24*30000000000*0.0016))*((5^3)-(2*5*1.3^2)+(1.3^3)))).

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

With Load per Unit Length (w^'), Distance x from Support (x), Elasticity Modulus of Concrete (E), Area Moment of Inertia (I) & Length of Beam (l) we can find Deflection at Any Point on Simply Supported Beam carrying UDL using the formula - Deflection of Beam = ((((Load per Unit Length*Distance x from Support)/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))*((Length of Beam^3)-(2*Length of Beam*Distance x from Support^2)+(Distance x from Support^3)))).

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*Length of Beam^2)/(16*Elasticity Modulus of Concrete*Area Moment of Inertia))
Deflection of Beam=(0.00651*(Uniformly Varying Load*(Length of Beam^4))/(Elasticity Modulus of Concrete*Area Moment of Inertia))
Deflection of Beam=(((Moment of Couple*Length of Beam*Distance x from Support)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia))*(1-((Distance x from Support^2)/(Length of Beam^2))))

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

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

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

Deflection at Any Point on Simply Supported 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 Simply Supported Beam carrying UDL can be measured.

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Deflection at Any Point on Simply Supported Beam carrying UDL Formula

​GoCenter Deflection of Simply Supported Beam carrying Couple Moment at Right End Formula

​GoCenter Deflection on Simply Supported Beam carrying UVL with Maximum Intensity at Right support Formula

Deflection at Any Point on Simply Supported Beam carrying UDL Example

Deflection at Any Point on Simply Supported Beam carrying UDL Solution

Deflection at Any Point on Simply Supported Beam carrying UDL Formula Elements

Other Formulas to find Deflection of Beam

Other formulas in Simply Supported Beam category

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

FAQs on Deflection at Any Point on Simply Supported Beam carrying UDL

Variable Name

GoCenter Deflection of Simply Supported Beam carrying Couple Moment at Right End Formula

GoCenter Deflection on Simply Supported Beam carrying UVL with Maximum Intensity at Right support Formula