Rotation due to Moment on Arch Dam Calculator

✖Moment acting on Arch Dam is an overturning effect (tends to bend or turn the member) created by the force(load) acting on a structural member.ⓘ Moment acting on Arch Dam [M_t]			+10% -10%
✖Constant K1 is defined as the constant depending on b/a ratio and Poisson ratio of an Arch Dam.ⓘ Constant K1 [K₁]			+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 Moment on Arch Dam [Φ]

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Rotation due to Moment on Arch Dam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch)
Φ = M_t*K₁/(E*t*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.
Moment acting on Arch Dam - (Measured in Joule) - Moment acting on Arch Dam is an overturning effect (tends to bend or turn the member) created by the force(load) acting on a structural member.
Constant K1 - Constant K1 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

Moment acting on Arch Dam: 54.5 Newton Meter --> 54.5 Joule (Check conversion here)
Constant K1: 10.01 --> 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 = M_t*K₁/(E*t*t) --> 54.5*10.01/(10.2*1.2*1.2)

Evaluating ... ...

Φ = 37.1422249455338

STEP 3: Convert Result to Output's Unit

37.1422249455338 Radian --> No Conversion Required

FINAL ANSWER

37.1422249455338 ≈ 37.14222 Radian <-- Angle of Rotation

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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NSS College of Engineering (NSSCE), Palakkad

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< Arch Dams Calculators

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

LaTeX 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

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

Intrados Stresses on Arch Dam

LaTeX 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

LaTeX 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 Moment on Arch Dam Formula

LaTeX 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)
Φ = M_t*K₁/(E*t*t)

What is Couple Moment ?

A couple is a system of forces with a resultant moment but no resultant force. A better term is force couple or pure moment. Its effect is to create rotation without translation, or more generally without any acceleration of the centre of mass.

How to Calculate Rotation due to Moment on Arch Dam?

Rotation due to Moment on Arch Dam calculator uses Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch) to calculate the Angle of Rotation, Rotation due to Moment on Arch Dam formula is defined as angle by which dam is tend to rotation due applied moment. Angle of Rotation is denoted by Φ symbol.

How to calculate Rotation due to Moment on Arch Dam using this online calculator? To use this online calculator for Rotation due to Moment on Arch Dam, enter Moment acting on Arch Dam (M_t), Constant K1 (K₁), Elastic Modulus of Rock (E) & Horizontal Thickness of an Arch (t) and hit the calculate button. Here is how the Rotation due to Moment on Arch Dam calculation can be explained with given input values -> 37.14222 = 54.5*10.01/(10.2*1.2*1.2).

FAQ

What is Rotation due to Moment on Arch Dam?

Rotation due to Moment on Arch Dam formula is defined as angle by which dam is tend to rotation due applied moment and is represented as Φ = M_t*K₁/(E*t*t) or Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch). Moment acting on Arch Dam is an overturning effect (tends to bend or turn the member) created by the force(load) acting on a structural member, Constant K1 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 Moment on Arch Dam?

Rotation due to Moment on Arch Dam formula is defined as angle by which dam is tend to rotation due applied moment is calculated using Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch). To calculate Rotation due to Moment on Arch Dam, you need Moment acting on Arch Dam (M_t), Constant K1 (K₁), Elastic Modulus of Rock (E) & Horizontal Thickness of an Arch (t). With our tool, you need to enter the respective value for Moment acting on Arch Dam, Constant K1, 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 Moment acting on Arch Dam, Constant K1, 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 = Cantilever Twisting Moment*Constant K4/(Elastic Modulus of Rock*Horizontal Thickness of an Arch^2)
Angle of Rotation = Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch)

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