Slope at Free End of Cantilever Beam Carrying Couple 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%

✖The Slope of Beam is the angle between deflected beam to the actual beam at the same point.ⓘ Slope at Free End of Cantilever Beam Carrying Couple at Free End [θ]

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Slope at Free End of Cantilever Beam Carrying Couple at Free End Solution

STEP 0: Pre-Calculation Summary

Formula Used

Slope of Beam = ((Moment of Couple*Length of Beam)/(Elasticity Modulus of Concrete*Area Moment of Inertia))
θ = ((M_c*l)/(E*I))
This formula uses 5 Variables

Variables Used

Slope of Beam - (Measured in Radian) - The Slope of Beam is the angle between deflected beam to the actual beam at the same point.
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

θ = ((M_c*l)/(E*I)) --> ((85000*5)/(30000000000*0.0016))

Evaluating ... ...

θ = 0.00885416666666667

STEP 3: Convert Result to Output's Unit

0.00885416666666667 Radian --> No Conversion Required

FINAL ANSWER

0.00885416666666667 ≈ 0.008854 Radian <-- Slope of Beam

(Calculation completed in 00.005 seconds)

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< 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)

Slope at Free End of Cantilever Beam Carrying Couple at Free End Formula

LaTeX Go

Slope of Beam = ((Moment of Couple*Length of Beam)/(Elasticity Modulus of Concrete*Area Moment of Inertia))
θ = ((M_c*l)/(E*I))

What is Slope of a Beam?

The Slope of a Beam is defined as the angle in radians which the tangent at the section makes with the original axis of the beam.

What is Moment of Couple?

The Moment of Couple is defined as the product of one of the two forces of a Couple and the perpendicular distance between their lines of action (called the arm of the Couple). The tendency of a force is to rotate a body. It is measured by the moment of the force.

How to Calculate Slope at Free End of Cantilever Beam Carrying Couple at Free End?

Slope at Free End of Cantilever Beam Carrying Couple at Free End calculator uses Slope of Beam = ((Moment of Couple*Length of Beam)/(Elasticity Modulus of Concrete*Area Moment of Inertia)) to calculate the Slope of Beam, The Slope at Free End of Cantilever Beam Carrying Couple at Free End formula is defined as angle between deflected beam to the actual beam at the same point due to couple at free end. Slope of Beam is denoted by θ symbol.

How to calculate Slope at Free End of Cantilever Beam Carrying Couple at Free End using this online calculator? To use this online calculator for Slope at Free End of Cantilever Beam Carrying Couple 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 Slope at Free End of Cantilever Beam Carrying Couple at Free End calculation can be explained with given input values -> 0.008854 = ((85000*5)/(30000000000*0.0016)).

FAQ

What is Slope at Free End of Cantilever Beam Carrying Couple at Free End?

The Slope at Free End of Cantilever Beam Carrying Couple at Free End formula is defined as angle between deflected beam to the actual beam at the same point due to couple at free end and is represented as θ = ((M_c*l)/(E*I)) or Slope of Beam = ((Moment of Couple*Length of Beam)/(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 Slope at Free End of Cantilever Beam Carrying Couple at Free End?

The Slope at Free End of Cantilever Beam Carrying Couple at Free End formula is defined as angle between deflected beam to the actual beam at the same point due to couple at free end is calculated using Slope of Beam = ((Moment of Couple*Length of Beam)/(Elasticity Modulus of Concrete*Area Moment of Inertia)). To calculate Slope at Free End of Cantilever Beam Carrying Couple 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 Slope of Beam?

In this formula, Slope 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 -

Slope of Beam = ((Load per Unit Length*Length of Beam^3)/(6*Elasticity Modulus of Concrete*Area Moment of Inertia))
Slope of Beam = ((Point Load*Distance x from Support^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))
Slope of Beam = ((Point Load*Length of Beam^2)/(2*Elasticity Modulus of Concrete*Area Moment of Inertia))

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