Rotation due to Shear on Arch Dam Calculator

✖Shear Force is the force which causes shear deformation to occur in the shear plane.ⓘ Shear Force [F_s]			+10% -10%
✖Constant K5 is defined as the constant depending on b/a ratio and Poisson ratio of an Arch Dam.ⓘ Constant K5 [K₅]			+10% -10%
✖Elastic Modulus of Rock is defined as the linear elastic deformation response of rock under deformation.ⓘ Elastic Modulus of Rock [E]			+10% -10%
✖Horizontal Thickness of an Arch, also known as the arch thickness or arch rise, refers to the distance between the intrados and the extrados along the horizontal axis.ⓘ Horizontal Thickness of an Arch [t]			+10% -10%

✖Angle of Rotation is defined as by how many degrees the object is moved with respect to reference line.ⓘ Rotation due to Shear on Arch Dam [Φ]

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Formula

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Rotation due to Shear on Arch Dam

Formula

`"Φ" = "F"_{"s"}*"K"_{"5"}/("E"*"t")`

Example

`"37.64297rad"="48.5N"*"9.5"/("10.2N/m²"*"1.2m")`

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Rotation due to Shear on Arch Dam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Rotation = Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch)
Φ = F_s*K₅/(E*t)
This formula uses 5 Variables

Variables Used

Angle of Rotation - (Measured in Radian) - Angle of Rotation is defined as by how many degrees the object is moved with respect to reference line.
Shear Force - (Measured in Newton) - Shear Force is the force which causes shear deformation to occur in the shear plane.
Constant K5 - Constant K5 is defined as the constant depending on b/a ratio and Poisson ratio of an Arch Dam.
Elastic Modulus of Rock - (Measured in Pascal) - Elastic Modulus of Rock is defined as the linear elastic deformation response of rock under deformation.
Horizontal Thickness of an Arch - (Measured in Meter) - Horizontal Thickness of an Arch, also known as the arch thickness or arch rise, refers to the distance between the intrados and the extrados along the horizontal axis.

STEP 1: Convert Input(s) to Base Unit

Shear Force: 48.5 Newton --> 48.5 Newton No Conversion Required
Constant K5: 9.5 --> No Conversion Required
Elastic Modulus of Rock: 10.2 Newton per Square Meter --> 10.2 Pascal (Check conversion here)
Horizontal Thickness of an Arch: 1.2 Meter --> 1.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ = F_s*K₅/(E*t) --> 48.5*9.5/(10.2*1.2)

Evaluating ... ...

Φ = 37.6429738562092

STEP 3: Convert Result to Output's Unit

37.6429738562092 Radian --> No Conversion Required

FINAL ANSWER

37.6429738562092 ≈ 37.64297 Radian <-- Angle of Rotation

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Dams » Arch Dams » Rotation due to Shear on Arch Dam

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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National Institute of Technology (NIT), Warangal

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< 9 Arch Dams Calculators

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam

Go Theta = acos((Thrust from Water-Radial Pressure*Radius to Center Line of Arch)/(-Radial Pressure*Radius to Center Line of Arch+Thrust of Abutments))

Radius to centerline given Thrust at Abutments of Arch Dam

Go Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure

Rotation due to Moment on Arch Dam

Go Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch)

Intrados Stresses on Arch Dam

Go Intrados Stresses = (Thrust of Abutments/Horizontal Thickness of an Arch)+(6*Moment acting on Arch Dam/(Horizontal Thickness of an Arch^2))

Extrados Stresses on Arch Dam

Go Intrados Stresses = (Thrust of Abutments/Horizontal Thickness of an Arch)-(6*Moment acting on Arch Dam/(Horizontal Thickness of an Arch^2))

Rotation due to Twist on Arch Dam

Go Angle of Rotation = Cantilever Twisting Moment*Constant K4/(Elastic Modulus of Rock*Horizontal Thickness of an Arch^2)

Shear Force given Rotation due to Shear on Arch Dam

Go Shear Force = Angle of Rotation*(Elastic Modulus of Rock*Horizontal Thickness of an Arch)/Constant K5

Rotation due to Shear on Arch Dam

Go Angle of Rotation = Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch)

Shear Force given Deflection due to Shear on Arch Dam

Go Shear Force = Deflection due to Moments on Arch Dam*Elastic Modulus of Rock/Constant K3

Rotation due to Shear on Arch Dam Formula

Angle of Rotation = Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch)
Φ = F_s*K₅/(E*t)

What is Shear Force ?

Shearing forces are unaligned forces pushing one part of a body in one specific direction, and another part of the body in the opposite direction. When the forces are colinear, they are called compression forces.

How to Calculate Rotation due to Shear on Arch Dam?

Rotation due to Shear on Arch Dam calculator uses Angle of Rotation = Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch) to calculate the Angle of Rotation, Rotation due to Shear on Arch Dam formula is defined as rotational deformation around abutments due to shear force. Angle of Rotation is denoted by Φ symbol.

How to calculate Rotation due to Shear on Arch Dam using this online calculator? To use this online calculator for Rotation due to Shear on Arch Dam, enter Shear Force (F_s), Constant K5 (K₅), Elastic Modulus of Rock (E) & Horizontal Thickness of an Arch (t) and hit the calculate button. Here is how the Rotation due to Shear on Arch Dam calculation can be explained with given input values -> 37.64297 = 48.5*9.5/(10.2*1.2).

FAQ

What is Rotation due to Shear on Arch Dam?

Rotation due to Shear on Arch Dam formula is defined as rotational deformation around abutments due to shear force and is represented as Φ = F_s*K₅/(E*t) or Angle of Rotation = Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch). Shear Force is the force which causes shear deformation to occur in the shear plane, Constant K5 is defined as the constant depending on b/a ratio and Poisson ratio of an Arch Dam, Elastic Modulus of Rock is defined as the linear elastic deformation response of rock under deformation & Horizontal Thickness of an Arch, also known as the arch thickness or arch rise, refers to the distance between the intrados and the extrados along the horizontal axis.

How to calculate Rotation due to Shear on Arch Dam?

Rotation due to Shear on Arch Dam formula is defined as rotational deformation around abutments due to shear force is calculated using Angle of Rotation = Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch). To calculate Rotation due to Shear on Arch Dam, you need Shear Force (F_s), Constant K5 (K₅), Elastic Modulus of Rock (E) & Horizontal Thickness of an Arch (t). With our tool, you need to enter the respective value for Shear Force, Constant K5, Elastic Modulus of Rock & Horizontal Thickness of an Arch 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 Angle of Rotation?

In this formula, Angle of Rotation uses Shear Force, Constant K5, Elastic Modulus of Rock & Horizontal Thickness of an Arch. We can use 2 other way(s) to calculate the same, which is/are as follows -

Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch)
Angle of Rotation = Cantilever Twisting Moment*Constant K4/(Elastic Modulus of Rock*Horizontal Thickness of an Arch^2)

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