Maximum Deflection of Cantilever Beam with Couple Moment at Free End Calculator

✖Moment of couple is equal to the product of either of forces and the perpendicular distance between the forces.ⓘ Moment of Couple [M_c]			+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 Deflection of Cantilever Beam with Couple Moment at Free End [δ]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Slope and Deflection Formulas PDF PDF Image

Maximum Deflection of Cantilever Beam with Couple Moment at Free End Solution

STEP 0: Pre-Calculation Summary

Formula Used

Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia)
δ = (M_c*(l^2))/(2*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.
Moment of Couple - (Measured in Newton Meter) - Moment of couple is equal to the product of either of forces and the perpendicular distance between the forces.
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

Moment of Couple: 85 Kilonewton Meter --> 85000 Newton Meter (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 = (M_c*(l^2))/(2*E*I) --> (85000*(5^2))/(2*30000000000*0.0016)

Evaluating ... ...

δ = 0.0221354166666667

STEP 3: Convert Result to Output's Unit

0.0221354166666667 Meter -->22.1354166666667 Millimeter (Check conversion here)

FINAL ANSWER

22.1354166666667 ≈ 22.13542 Millimeter <-- Deflection of Beam

(Calculation completed in 00.020 seconds)

You are here -

Home » Engineering » Civil » Strength of Materials » Slope and Deflection » Cantilever Beam » Maximum Deflection of Cantilever Beam with Couple Moment at Free End

Credits

Created by Alithea Fernandes

Don Bosco College of Engineering (DBCE), Goa

Alithea Fernandes has created this Calculator and 100+ more calculators!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has verified this Calculator and 1800+ more calculators!

< Cantilever Beam Calculators

Deflection at Any Point on Cantilever Beam carrying UDL

LaTeX Go Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)-(4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia)))

Deflection of Cantilever Beam carrying Point Load at Any Point

LaTeX Go Deflection of Beam = (Point Load*(Distance from Support A^2)*(3*Length of Beam-Distance from Support A))/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)

Deflection at Any Point on Cantilever Beam carrying Couple Moment at Free End

LaTeX Go Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))

Maximum Deflection of Cantilever Beam carrying Point Load at Free End

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

Maximum Deflection of Cantilever Beam with Couple Moment at Free End Formula

LaTeX Go

Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia)
δ = (M_c*(l^2))/(2*E*I)

What is Maximum and Center Deflection of Cantilever Beam with Couple Moment at Free End?

The Maximum and Center Deflection of Cantilever Beam with Couple Moment at Free End is the degree to which a cantilever beam is displaced under a couple moment

How to Calculate Maximum Deflection of Cantilever Beam with Couple Moment at Free End?

Maximum Deflection of Cantilever Beam with Couple Moment at Free End calculator uses Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia) to calculate the Deflection of Beam, The Maximum Deflection of Cantilever Beam with Couple Moment at Free End formula is defined as (Couple Moment*(length of the beam^2))/(2*Modulus of Elasticity*Area Moment of inertia). Deflection of Beam is denoted by δ symbol.

How to calculate Maximum Deflection of Cantilever Beam with Couple Moment at Free End using this online calculator? To use this online calculator for Maximum Deflection of Cantilever Beam with Couple Moment at Free End, enter Moment of Couple (M_c), Length of Beam (l), Elasticity Modulus of Concrete (E) & Area Moment of Inertia (I) and hit the calculate button. Here is how the Maximum Deflection of Cantilever Beam with Couple Moment at Free End calculation can be explained with given input values -> 22135.42 = (85000*(5^2))/(2*30000000000*0.0016).

FAQ

What is Maximum Deflection of Cantilever Beam with Couple Moment at Free End?

The Maximum Deflection of Cantilever Beam with Couple Moment at Free End formula is defined as (Couple Moment*(length of the beam^2))/(2*Modulus of Elasticity*Area Moment of inertia) and is represented as δ = (M_c*(l^2))/(2*E*I) or Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia). Moment of couple is equal to the product of either of forces and the perpendicular distance between the forces, 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 Deflection of Cantilever Beam with Couple Moment at Free End?

The Maximum Deflection of Cantilever Beam with Couple Moment at Free End formula is defined as (Couple Moment*(length of the beam^2))/(2*Modulus of Elasticity*Area Moment of inertia) is calculated using Deflection of Beam = (Moment of Couple*(Length of Beam^2))/(2*Elasticity Modulus of Concrete*Area Moment of Inertia). To calculate Maximum Deflection of Cantilever Beam with Couple Moment at Free End, you need Moment of Couple (M_c), 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 Moment of Couple, 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 Moment of Couple, Length of Beam, Elasticity Modulus of Concrete & Area Moment of Inertia. We can use 3 other way(s) to calculate the same, which is/are as follows -

Deflection of Beam = ((Load per Unit Length*Distance x from Support^2)*(((Distance x from Support^2)+(6*Length of Beam^2)-(4*Distance x from Support*Length of Beam))/(24*Elasticity Modulus of Concrete*Area Moment of Inertia)))
Deflection of Beam = ((Moment of Couple*Distance x from Support^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))
Deflection of Beam = (Point Load*(Distance from Support A^2)*(3*Length of Beam-Distance from Support A))/(6*Elasticity Modulus of Concrete*Area Moment of Inertia)

Home

FREE PDFs

🔍 Search