Moments given Intrados Stresses on Arch Dam Solution

STEP 0: Pre-Calculation Summary
Formula Used
Moment acting on Arch Dam = (Intrados Stresses*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch-Thrust of Abutments*Horizontal Thickness of an Arch)/6
Mt = (S*t*t-F*t)/6
This formula uses 4 Variables
Variables Used
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.
Intrados Stresses - (Measured in Pascal) - Intrados Stresses is defined as the stresses on the inner wall of the Arch Dam.
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.
Thrust of Abutments - (Measured in Newton) - Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.
STEP 1: Convert Input(s) to Base Unit
Intrados Stresses: 250 Newton per Square Meter --> 250 Pascal (Check conversion here)
Horizontal Thickness of an Arch: 1.2 Meter --> 1.2 Meter No Conversion Required
Thrust of Abutments: 63.55 Newton --> 63.55 Newton No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Mt = (S*t*t-F*t)/6 --> (250*1.2*1.2-63.55*1.2)/6
Evaluating ... ...
Mt = 47.29
STEP 3: Convert Result to Output's Unit
47.29 Joule -->47.29 Newton Meter (Check conversion here)
FINAL ANSWER
47.29 Newton Meter <-- Moment acting on Arch Dam
(Calculation completed in 00.020 seconds)

Credits

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National Institute of Technology Karnataka (NITK), Surathkal
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NSS College of Engineering (NSSCE), Palakkad
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7 Moments acting on Arch Dam Calculators

Moment at Abutments of Arch Dam
Go Moment acting on Arch Dam = Radius to Center Line of Arch*((Normal Radial Pressure*Radius to Center Line of Arch)-Thrust of Abutments)*(sin(Angle between Crown and Abundant Radii)/(Angle between Crown and Abundant Radii)-cos(Angle between Crown and Abundant Radii))
Moment at Crown of Arch Dam
Go Moment acting on Arch Dam = -Radius to Center Line of Arch*((Normal Radial Pressure*Radius to Center Line of Arch)-Thrust of Abutments)*(1-((sin(Angle between Crown and Abundant Radii))/Angle between Crown and Abundant Radii))
Moments given Intrados Stresses on Arch Dam
Go Moment acting on Arch Dam = (Intrados Stresses*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch-Thrust of Abutments*Horizontal Thickness of an Arch)/6
Moments given Extrados Stresses on Arch Dam
Go Moment acting on Arch Dam = Extrados Stress*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch+Thrust of Abutments*Horizontal Thickness of an Arch/6
Moments given Rotation due to Moment on Arch Dam
Go Moment acting on Arch Dam = (Angle of Rotation*(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch))/Constant K1
Moments given Deflection due to Moments on Arch Dam
Go Moment acting on Arch Dam = Deflection due to Moments on Arch Dam*(Elastic Modulus of Rock*Horizontal Thickness of an Arch)/Constant K5
Moments given Rotation due to Twist on Arch Dam
Go Cantilever Twisting Moment = (Elastic Modulus of Rock*Horizontal Thickness of an Arch^2)*Angle of Rotation/Constant K4

Moments given Intrados Stresses on Arch Dam Formula

Moment acting on Arch Dam = (Intrados Stresses*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch-Thrust of Abutments*Horizontal Thickness of an Arch)/6
Mt = (S*t*t-F*t)/6

What is an Arch Dam ?

An arch dam is a concrete dam that is curved upstream in plan. The arch dam is designed so that the force of the water against it, known as hydrostatic pressure, presses against the arch, causing the arch to straighten slightly and strengthening the structure as it pushes into its foundation or abutments.

How to Calculate Moments given Intrados Stresses on Arch Dam?

Moments given Intrados Stresses on Arch Dam calculator uses Moment acting on Arch Dam = (Intrados Stresses*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch-Thrust of Abutments*Horizontal Thickness of an Arch)/6 to calculate the Moment acting on Arch Dam, Moments given Intrados Stresses on Arch Dam is defined as couple produced on inner wall of dam. Moment acting on Arch Dam is denoted by Mt symbol.

How to calculate Moments given Intrados Stresses on Arch Dam using this online calculator? To use this online calculator for Moments given Intrados Stresses on Arch Dam, enter Intrados Stresses (S), Horizontal Thickness of an Arch (t) & Thrust of Abutments (F) and hit the calculate button. Here is how the Moments given Intrados Stresses on Arch Dam calculation can be explained with given input values -> 47.29 = (250*1.2*1.2-63.55*1.2)/6.

FAQ

What is Moments given Intrados Stresses on Arch Dam?
Moments given Intrados Stresses on Arch Dam is defined as couple produced on inner wall of dam and is represented as Mt = (S*t*t-F*t)/6 or Moment acting on Arch Dam = (Intrados Stresses*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch-Thrust of Abutments*Horizontal Thickness of an Arch)/6. Intrados Stresses is defined as the stresses on the inner wall of the Arch Dam, 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 & Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.
How to calculate Moments given Intrados Stresses on Arch Dam?
Moments given Intrados Stresses on Arch Dam is defined as couple produced on inner wall of dam is calculated using Moment acting on Arch Dam = (Intrados Stresses*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch-Thrust of Abutments*Horizontal Thickness of an Arch)/6. To calculate Moments given Intrados Stresses on Arch Dam, you need Intrados Stresses (S), Horizontal Thickness of an Arch (t) & Thrust of Abutments (F). With our tool, you need to enter the respective value for Intrados Stresses, Horizontal Thickness of an Arch & Thrust of Abutments 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 Moment acting on Arch Dam?
In this formula, Moment acting on Arch Dam uses Intrados Stresses, Horizontal Thickness of an Arch & Thrust of Abutments. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Moment acting on Arch Dam = -Radius to Center Line of Arch*((Normal Radial Pressure*Radius to Center Line of Arch)-Thrust of Abutments)*(1-((sin(Angle between Crown and Abundant Radii))/Angle between Crown and Abundant Radii))
  • Moment acting on Arch Dam = Radius to Center Line of Arch*((Normal Radial Pressure*Radius to Center Line of Arch)-Thrust of Abutments)*(sin(Angle between Crown and Abundant Radii)/(Angle between Crown and Abundant Radii)-cos(Angle between Crown and Abundant Radii))
  • Moment acting on Arch Dam = Extrados Stress*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch+Thrust of Abutments*Horizontal Thickness of an Arch/6
  • Moment acting on Arch Dam = (Angle of Rotation*(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch))/Constant K1
  • Moment acting on Arch Dam = Deflection due to Moments on Arch Dam*(Elastic Modulus of Rock*Horizontal Thickness of an Arch)/Constant K5
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