Moment at Crown of Arch Dam Calculator

✖Radius to Center Line of Arch is a radial line from the focus to any point of a curve.ⓘ Radius to Center Line of Arch [r]			+10% -10%
✖Normal Radial Pressure at the center line is the extrados pressure times the ratio of the upstream radius to the center-line radius.ⓘ Normal Radial Pressure [p]			+10% -10%
✖Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.ⓘ Thrust of Abutments [F]			+10% -10%
✖Angle between Crown and Abundant radii is the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.ⓘ Angle between Crown and Abundant Radii [A]			+10% -10%

✖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 at Crown of Arch Dam [M_t]

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Moment at Crown of Arch Dam Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
M_t = -r*((p*r)-F)*(1-((sin(A))/A))
This formula uses 1 Functions, 5 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

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.
Radius to Center Line of Arch - (Measured in Meter) - Radius to Center Line of Arch is a radial line from the focus to any point of a curve.
Normal Radial Pressure - Normal Radial Pressure at the center line is the extrados pressure times the ratio of the upstream radius to the center-line radius.
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.
Angle between Crown and Abundant Radii - (Measured in Radian) - Angle between Crown and Abundant radii is the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.

STEP 1: Convert Input(s) to Base Unit

Radius to Center Line of Arch: 5.5 Meter --> 5.5 Meter No Conversion Required
Normal Radial Pressure: 8 --> No Conversion Required
Thrust of Abutments: 63.55 Newton --> 63.55 Newton No Conversion Required
Angle between Crown and Abundant Radii: 31 Radian --> 31 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_t = -r*((p*r)-F)*(1-((sin(A))/A)) --> -5.5*((8*5.5)-63.55)*(1-((sin(31))/31))

Evaluating ... ...

M_t = 108.926424123012

STEP 3: Convert Result to Output's Unit

108.926424123012 Joule -->108.926424123012 Newton Meter (Check conversion here)

FINAL ANSWER

108.926424123012 ≈ 108.9264 Newton Meter <-- Moment acting on Arch Dam

(Calculation completed in 00.013 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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< Moments acting on Arch Dam Calculators

Moment at Abutments of Arch Dam

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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

Moment at Crown of Arch Dam Formula

LaTeX Go

What is 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 Moment at Crown of Arch Dam?

Moment at Crown of Arch Dam calculator uses 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)) to calculate the Moment acting on Arch Dam, The Moment at Crown of Arch Dam is defined as moment generated due to thrust acting on dam, at top most point. Moment acting on Arch Dam is denoted by M_t symbol.

How to calculate Moment at Crown of Arch Dam using this online calculator? To use this online calculator for Moment at Crown of Arch Dam, enter Radius to Center Line of Arch (r), Normal Radial Pressure (p), Thrust of Abutments (F) & Angle between Crown and Abundant Radii (A) and hit the calculate button. Here is how the Moment at Crown of Arch Dam calculation can be explained with given input values -> 108.9264 = -5.5*((8*5.5)-63.55)*(1-((sin(31))/31)).

FAQ

What is Moment at Crown of Arch Dam?

The Moment at Crown of Arch Dam is defined as moment generated due to thrust acting on dam, at top most point and is represented as M_t = -r*((p*r)-F)*(1-((sin(A))/A)) or 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)). Radius to Center Line of Arch is a radial line from the focus to any point of a curve, Normal Radial Pressure at the center line is the extrados pressure times the ratio of the upstream radius to the center-line radius, Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments & Angle between Crown and Abundant radii is the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.

How to calculate Moment at Crown of Arch Dam?

The Moment at Crown of Arch Dam is defined as moment generated due to thrust acting on dam, at top most point is calculated using 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)). To calculate Moment at Crown of Arch Dam, you need Radius to Center Line of Arch (r), Normal Radial Pressure (p), Thrust of Abutments (F) & Angle between Crown and Abundant Radii (A). With our tool, you need to enter the respective value for Radius to Center Line of Arch, Normal Radial Pressure, Thrust of Abutments & Angle between Crown and Abundant Radii 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 Radius to Center Line of Arch, Normal Radial Pressure, Thrust of Abutments & Angle between Crown and Abundant Radii. We can use 3 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)*(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 = (Intrados Stresses*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch-Thrust of Abutments*Horizontal Thickness of an Arch)/6
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

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