Deflection at Any Point on Simply Supported Beam carrying UDL Calculator

✖Load per Unit Length is the load distributed per unit meter.ⓘ Load per Unit Length [w^']			+10% -10%
✖Distance x from Support is the length of a beam from the support to any point on the beam.ⓘ Distance x from Support [x]			+10% -10%
✖Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain.ⓘ Elasticity Modulus of Concrete [E]			+10% -10%
✖Area Moment of Inertia is a moment about the centroidal axis without considering mass.ⓘ Area Moment of Inertia [I]			+10% -10%
✖Length of Beam is defined as the distance between the supports.ⓘ Length of Beam [l]			+10% -10%

✖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.ⓘ Deflection at Any Point on Simply Supported Beam carrying UDL [δ]

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Deflection at Any Point on Simply Supported Beam carrying UDL

Formula

`"δ" = (((("w"^{"'"}*"x")/(24*"E"*"I"))*(("l"^3)-(2*"l"*"x"^2)+("x"^3))))`

Example

`"2.98721mm"=(((("24kN/m"*"1300mm")/(24*"30000MPa"*"0.0016m⁴"))*((("5000mm")^3)-(2*"5000mm"*("1300mm")^2)+(("1300mm")^3))))`

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Deflection at Any Point on Simply Supported Beam carrying UDL Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))))
δ = ((((w^'*x)/(24*E*I))*((l^3)-(2*l*x^2)+(x^3))))
This formula uses 6 Variables

Variables Used

Deflection of Beam - (Measured in Meter) - 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.
Load per Unit Length - (Measured in Newton per Meter) - Load per Unit Length is the load distributed per unit meter.
Distance x from Support - (Measured in Meter) - Distance x from Support is the length of a beam from the support to any point on the beam.
Elasticity Modulus of Concrete - (Measured in Pascal) - Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain.
Area Moment of Inertia - (Measured in Meter⁴) - Area Moment of Inertia is a moment about the centroidal axis without considering mass.
Length of Beam - (Measured in Meter) - Length of Beam is defined as the distance between the supports.

STEP 1: Convert Input(s) to Base Unit

Load per Unit Length: 24 Kilonewton per Meter --> 24000 Newton per Meter (Check conversion here)
Distance x from Support: 1300 Millimeter --> 1.3 Meter (Check conversion here)
Elasticity Modulus of Concrete: 30000 Megapascal --> 30000000000 Pascal (Check conversion here)
Area Moment of Inertia: 0.0016 Meter⁴ --> 0.0016 Meter⁴ No Conversion Required
Length of Beam: 5000 Millimeter --> 5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = ((((w^'*x)/(24*E*I))*((l^3)-(2*l*x^2)+(x^3)))) --> ((((24000*1.3)/(24*30000000000*0.0016))*((5^3)-(2*5*1.3^2)+(1.3^3))))

Evaluating ... ...

δ = 0.00298721041666667

STEP 3: Convert Result to Output's Unit

0.00298721041666667 Meter -->2.98721041666667 Millimeter (Check conversion here)

FINAL ANSWER

2.98721041666667 ≈ 2.98721 Millimeter <-- Deflection of Beam

(Calculation completed in 00.004 seconds)

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< 15 Simply Supported Beam Calculators

Deflection at Any Point on Simply Supported Beam carrying UDL

Go 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))))

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

Go 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))))

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

Go Deflection of Beam = (0.00651*(Uniformly Varying Load*(Length of Beam^4))/(Elasticity Modulus of Concrete*Area Moment of Inertia))

Maximum Deflection on Simply Supported Beam carrying UVL Max Intensity at Right Support

Go Deflection of Beam = (0.00652*(Uniformly Varying Load*(Length of Beam^4))/(Elasticity Modulus of Concrete*Area Moment of Inertia))

Maximum Deflection of Simply Supported Beam carrying Triangular Load with Max Intensity at Center

Go Deflection of Beam = (((Uniformly Varying Load*(Length of Beam^4))/(120*Elasticity Modulus of Concrete*Area Moment of Inertia)))

Maximum and Center Deflection of Simply Supported Beam carrying UDL over its Entire Length

Go Deflection of Beam = (5*Load per Unit Length*(Length of Beam^4))/(384*Elasticity Modulus of Concrete*Area Moment of Inertia)

Maximum Deflection of Simply Supported Beam carrying Couple Moment at Right End

Go Deflection of Beam = ((Moment of Couple*Length of Beam^2)/(15.5884*Elasticity Modulus of Concrete*Area Moment of Inertia))

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

Go Slope of Beam = ((7*Uniformly Varying Load*Length of Beam^3)/(360*Elasticity Modulus of Concrete*Area Moment of Inertia))

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

Go Slope of Beam = ((Uniformly Varying Load*Length of Beam^3)/(45*Elasticity Modulus of Concrete*Area Moment of Inertia))

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

Go Deflection of Beam = ((Moment of Couple*Length of Beam^2)/(16*Elasticity Modulus of Concrete*Area Moment of Inertia))

Slope at Free Ends of Simply Supported Beam carrying UDL

Go Slope of Beam = ((Load per Unit Length*Length of Beam^3)/(24*Elasticity Modulus of Concrete*Area Moment of Inertia))

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

Go Deflection of Beam = (Point Load*(Length of Beam^3))/(48*Elasticity Modulus of Concrete*Area Moment of Inertia)

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

Go Slope of Beam = ((Moment of Couple*Length of Beam)/(3*Elasticity Modulus of Concrete*Area Moment of Inertia))

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

Go Slope of Beam = ((Moment of Couple*Length of Beam)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia))

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

Go Slope of Beam = ((Point Load*Length of Beam^2)/(16*Elasticity Modulus of Concrete*Area Moment of Inertia))

Deflection at Any Point on Simply Supported Beam carrying UDL Formula

What is Beam Deflection?

The deformation of a Beam is usually expressed in terms of its deflection from its original unloaded position. The deflection is measured from the original neutral surface of the beam to the neutral surface of the deformed beam. The configuration assumed by the deformed neutral surface is known as the elastic curve of the beam.

What is UDL?

The Uniformly Distributed Load (UDL) is a load that is distributed or spread across the whole region of an element such as a beam or slab. In other words, the magnitude of the load remains uniform throughout the whole element.

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

Deflection at Any Point on Simply Supported Beam carrying UDL calculator 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 calculate 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 calculate Deflection at Any Point on Simply Supported Beam carrying UDL using this online calculator? To use this online calculator 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. Here is how the Deflection at Any Point on Simply Supported Beam carrying UDL calculation can be explained with given input values -> 2987.21 = ((((24000*1.3)/(24*30000000000*0.0016))*((5^3)-(2*5*1.3^2)+(1.3^3)))).

FAQ

What is Deflection at Any Point on Simply Supported Beam carrying UDL?

The Deflection at Any Point on Simply Supported Beam carrying UDL formula is defined as the distance between its position before and after loading and is represented as δ = ((((w^'*x)/(24*E*I))*((l^3)-(2*l*x^2)+(x^3)))) or 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)))). Load per Unit Length is the load distributed per unit meter, Distance x from Support is the length of a beam from the support to any point on the beam, Elasticity modulus of Concrete (Ec) is the ratio of the applied stress to the corresponding strain, Area Moment of Inertia is a moment about the centroidal axis without considering mass & Length of Beam is defined as the distance between the supports.

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

The Deflection at Any Point on Simply Supported Beam carrying UDL formula is defined as the distance between its position before and after loading is calculated using 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 calculate Deflection at Any Point on Simply Supported Beam carrying UDL, you need Load per Unit Length (w^'), Distance x from Support (x), Elasticity Modulus of Concrete (E), Area Moment of Inertia (I) & Length of Beam (l). With our tool, you need to enter the respective value for Load per Unit Length, Distance x from Support, Elasticity Modulus of Concrete, Area Moment of Inertia & Length of Beam and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Deflection of Beam?

In this formula, Deflection of Beam uses Load per Unit Length, Distance x from Support, Elasticity Modulus of Concrete, Area Moment of Inertia & Length of Beam. We can use 8 other way(s) to calculate the same, which is/are as follows -

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))))
Deflection of Beam = (Point Load*(Length of Beam^3))/(48*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = (5*Load per Unit Length*(Length of Beam^4))/(384*Elasticity Modulus of Concrete*Area Moment of Inertia)
Deflection of Beam = ((Moment of Couple*Length of Beam^2)/(15.5884*Elasticity Modulus of Concrete*Area Moment of Inertia))
Deflection of Beam = (((Uniformly Varying Load*(Length of Beam^4))/(120*Elasticity Modulus of Concrete*Area Moment of Inertia)))
Deflection of Beam = (0.00652*(Uniformly Varying Load*(Length of Beam^4))/(Elasticity Modulus of Concrete*Area Moment of Inertia))

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