Moment at Abutments 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 Abutments of Arch Dam [M_t]

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Formula

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Moment at Abutments of Arch Dam

Formula

`"M"_{"t"} = "r"*(("p"*"r")-"F")*(sin("A")/("A")-cos("A"))`

Example

`"99.7591N*m"="5.5m"*(("8"*"5.5m")-"63.55N")*(sin("31rad")/("31rad")-cos("31rad"))`

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Moment at Abutments 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)*(sin(Angle between Crown and Abundant Radii)/(Angle between Crown and Abundant Radii)-cos(Angle between Crown and Abundant Radii))
M_t = r*((p*r)-F)*(sin(A)/(A)-cos(A))
This formula uses 2 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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(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)*(sin(A)/(A)-cos(A)) --> 5.5*((8*5.5)-63.55)*(sin(31)/(31)-cos(31))

Evaluating ... ...

M_t = 99.7590961459439

STEP 3: Convert Result to Output's Unit

99.7590961459439 Joule -->99.7590961459439 Newton Meter (Check conversion here)

FINAL ANSWER

99.7590961459439 ≈ 99.7591 Newton Meter <-- Moment acting on Arch Dam

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Dams » Arch Dams » Moments acting on Arch Dam » Moment at Abutments of Arch Dam

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

Rithik Agrawal has created this Calculator and 1300+ more calculators!

Verified by Chandana P Dev

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

Moment at Abutments of Arch Dam Formula

What are Abutments ?

An abutment is the substructure at the ends of a bridge span or dam supporting its superstructure. Single-span bridges have abutments at each end which provide vertical and lateral support for the span, as well as acting as retaining walls to resist lateral movement of the earthen fill of the bridge approach.

How to Calculate Moment at Abutments of Arch Dam?

Moment at Abutments 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)*(sin(Angle between Crown and Abundant Radii)/(Angle between Crown and Abundant Radii)-cos(Angle between Crown and Abundant Radii)) to calculate the Moment acting on Arch Dam, The Moment at Abutments of Arch Dam formula is defined as moment acting due to thrust on side walls of dams. Moment acting on Arch Dam is denoted by M_t symbol.

How to calculate Moment at Abutments of Arch Dam using this online calculator? To use this online calculator for Moment at Abutments 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 Abutments of Arch Dam calculation can be explained with given input values -> 99.7591 = 5.5*((8*5.5)-63.55)*(sin(31)/(31)-cos(31)).

FAQ

What is Moment at Abutments of Arch Dam?

The Moment at Abutments of Arch Dam formula is defined as moment acting due to thrust on side walls of dams and is represented as M_t = r*((p*r)-F)*(sin(A)/(A)-cos(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)*(sin(Angle between Crown and Abundant Radii)/(Angle between Crown and Abundant Radii)-cos(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 Abutments of Arch Dam?

The Moment at Abutments of Arch Dam formula is defined as moment acting due to thrust on side walls of dams 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)*(sin(Angle between Crown and Abundant Radii)/(Angle between Crown and Abundant Radii)-cos(Angle between Crown and Abundant Radii)). To calculate Moment at Abutments 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 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 = (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
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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