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

✖Point Load acting on a beam is a force applied at a single point at a set distance from the ends of the beam.ⓘ Point Load [P]			+10% -10%
✖Length of Beam is defined as the distance between the supports.ⓘ Length of Beam [l]			+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%

✖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.ⓘ Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center [δ]

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

Formula

`"δ" = ("P"*("l"^3))/(48*"E"*"I")`

Example

`"4.774306mm"=("88kN"*(("5000mm")^3))/(48*"30000MPa"*"0.0016m⁴")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Beam = (Point Load*(Length of Beam^3))/(48*Elasticity Modulus of Concrete*Area Moment of Inertia)
δ = (P*(l^3))/(48*E*I)
This formula uses 5 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.
Point Load - (Measured in Newton) - Point Load acting on a beam is a force applied at a single point at a set distance from the ends of the beam.
Length of Beam - (Measured in Meter) - Length of Beam is defined as the distance between the supports.
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.

STEP 1: Convert Input(s) to Base Unit

Point Load: 88 Kilonewton --> 88000 Newton (Check conversion here)
Length of Beam: 5000 Millimeter --> 5 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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

δ = (P*(l^3))/(48*E*I) --> (88000*(5^3))/(48*30000000000*0.0016)

Evaluating ... ...

δ = 0.00477430555555556

STEP 3: Convert Result to Output's Unit

0.00477430555555556 Meter -->4.77430555555556 Millimeter (Check conversion here)

FINAL ANSWER

4.77430555555556 ≈ 4.774306 Millimeter <-- Deflection of Beam

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Strength of Materials » Slope and Deflection » Simply Supported Beam » Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center

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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))

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

Deflection of Beam = (Point Load*(Length of Beam^3))/(48*Elasticity Modulus of Concrete*Area Moment of Inertia)
δ = (P*(l^3))/(48*E*I)

What is Maximum and Center Deflection of Simply Supported Beam carrying Point Load?

The Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center is the maximum degree to which a Beam is displaced at the center due to a point load

How to Calculate Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center?

Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center calculator uses Deflection of Beam = (Point Load*(Length of Beam^3))/(48*Elasticity Modulus of Concrete*Area Moment of Inertia) to calculate the Deflection of Beam, The Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center formula is defined as (Point Load acting on Beam*(Length of Beam^3))/(48*Modulus of Elasticity*Area Moment of Inertia). Deflection of Beam is denoted by δ symbol.

How to calculate Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center using this online calculator? To use this online calculator for Maximum and Center Deflection of Simply Supported Beam carrying Point 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. Here is how the Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center calculation can be explained with given input values -> 4774.306 = (88000*(5^3))/(48*30000000000*0.0016).

FAQ

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

The Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center formula is defined as (Point Load acting on Beam*(Length of Beam^3))/(48*Modulus of Elasticity*Area Moment of Inertia) and is represented as δ = (P*(l^3))/(48*E*I) or Deflection of Beam = (Point Load*(Length of Beam^3))/(48*Elasticity Modulus of Concrete*Area Moment of Inertia). Point Load acting on a beam is a force applied at a single point at a set distance from the ends of the beam, Length of Beam is defined as the distance between the supports, 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.

How to calculate Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center?

The Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center formula is defined as (Point Load acting on Beam*(Length of Beam^3))/(48*Modulus of Elasticity*Area Moment of Inertia) is calculated using Deflection of Beam = (Point Load*(Length of Beam^3))/(48*Elasticity Modulus of Concrete*Area Moment of Inertia). To calculate Maximum and Center Deflection of Simply Supported Beam carrying Point Load at Center, you need Point Load (P), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I). With our tool, you need to enter the respective value for Point Load, Length of Beam, Elasticity Modulus of Concrete & Area Moment of Inertia 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 Point Load, Length of Beam, Elasticity Modulus of Concrete & Area Moment of Inertia. 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 = ((((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 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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