Thrust at Crown of Arch Dam Calculator

✖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%
✖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%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ]			+10% -10%
✖Base Thickness is the maximum thickness or width of a dam measured horizontally between upstream and downstream faces and normal to the axis or centerline crest of the dam.ⓘ Base Thickness [T_b]			+10% -10%
✖Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.ⓘ Diameter [D]			+10% -10%

✖Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.ⓘ Thrust at Crown of Arch Dam [F]

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Formula

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Thrust at Crown of Arch Dam

Formula

`"F" = ("p"*"r")*(1-(2*"θ"*sin("θ"*(("T"_{"b"}/"r")^2)/12)/"D"))`

Example

`"43.98877N"=("8"*"5.5m")*(1-(2*"30°"*sin("30°"*(("1.3m"/"5.5m")^2)/12)/"9.999m"))`

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Thrust at Crown of Arch Dam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thrust of Abutments = (Normal Radial Pressure*Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Base Thickness/Radius to Center Line of Arch)^2)/12)/Diameter))
F = (p*r)*(1-(2*θ*sin(θ*((T_b/r)^2)/12)/D))
This formula uses 1 Functions, 6 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

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.
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.
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.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
Base Thickness - (Measured in Meter) - Base Thickness is the maximum thickness or width of a dam measured horizontally between upstream and downstream faces and normal to the axis or centerline crest of the dam.
Diameter - (Measured in Meter) - Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.

STEP 1: Convert Input(s) to Base Unit

Normal Radial Pressure: 8 --> No Conversion Required
Radius to Center Line of Arch: 5.5 Meter --> 5.5 Meter No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Base Thickness: 1.3 Meter --> 1.3 Meter No Conversion Required
Diameter: 9.999 Meter --> 9.999 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F = (p*r)*(1-(2*θ*sin(θ*((T_b/r)^2)/12)/D)) --> (8*5.5)*(1-(2*0.5235987755982*sin(0.5235987755982*((1.3/5.5)^2)/12)/9.999))

Evaluating ... ...

F = 43.9887668127631

STEP 3: Convert Result to Output's Unit

43.9887668127631 Newton --> No Conversion Required

FINAL ANSWER

43.9887668127631 ≈ 43.98877 Newton <-- Thrust of Abutments

(Calculation completed in 00.013 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Dams » Arch Dams » Thrust on Arch Dam » Thrust at Crown of Arch Dam

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Coorg Institute of Technology (CIT), Coorg

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< 6 Thrust on Arch Dam Calculators

Thrust at Crown of Arch Dam given Moment at Abutments

Go Thrust of Abutments = Moment acting on Arch Dam/(Radius to Center Line of Arch*(sin(Theta)/(Theta-(cos(Theta)))))+Normal Radial Pressure*Radius to Center Line of Arch

Thrust at Crown of Arch Dam

Go Thrust of Abutments = (Normal Radial Pressure*Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Base Thickness/Radius to Center Line of Arch)^2)/12)/Diameter))

Thrust at Abutments of Arch Dam

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

Thrust given Extrados Stresses on Arch Dam

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

Thrust given Intrados Stresses on Arch Dam

Go Thrust of Abutments = Intrados Stresses*Base Thickness-6*Moment acting on Arch Dam/Base Thickness

Thrust given Deflection due to Thrust on Arch Dam

Go Thrust of Abutments = Deflection due to Moments on Arch Dam*Elastic Modulus of Rock/Constant K2

Thrust at Crown of Arch Dam Formula

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 Thrust at Crown of Arch Dam?

Thrust at Crown of Arch Dam calculator uses Thrust of Abutments = (Normal Radial Pressure*Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Base Thickness/Radius to Center Line of Arch)^2)/12)/Diameter)) to calculate the Thrust of Abutments, The Thrust at Crown of Arch Dam is defined as the horizontal force exerted by the water pressure on the curved upstream face of an arch dam, acting perpendicular to the dam axis at its highest point. Thrust of Abutments is denoted by F symbol.

How to calculate Thrust at Crown of Arch Dam using this online calculator? To use this online calculator for Thrust at Crown of Arch Dam, enter Normal Radial Pressure (p), Radius to Center Line of Arch (r), Theta (θ), Base Thickness (T_b) & Diameter (D) and hit the calculate button. Here is how the Thrust at Crown of Arch Dam calculation can be explained with given input values -> 43.98877 = (8*5.5)*(1-(2*0.5235987755982*sin(0.5235987755982*((1.3/5.5)^2)/12)/9.999)).

FAQ

What is Thrust at Crown of Arch Dam?

The Thrust at Crown of Arch Dam is defined as the horizontal force exerted by the water pressure on the curved upstream face of an arch dam, acting perpendicular to the dam axis at its highest point and is represented as F = (p*r)*(1-(2*θ*sin(θ*((T_b/r)^2)/12)/D)) or Thrust of Abutments = (Normal Radial Pressure*Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Base Thickness/Radius to Center Line of Arch)^2)/12)/Diameter)). Normal Radial Pressure at the center line is the extrados pressure times the ratio of the upstream radius to the center-line radius, Radius to Center Line of Arch is a radial line from the focus to any point of a curve, Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint, Base Thickness is the maximum thickness or width of a dam measured horizontally between upstream and downstream faces and normal to the axis or centerline crest of the dam & Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.

How to calculate Thrust at Crown of Arch Dam?

The Thrust at Crown of Arch Dam is defined as the horizontal force exerted by the water pressure on the curved upstream face of an arch dam, acting perpendicular to the dam axis at its highest point is calculated using Thrust of Abutments = (Normal Radial Pressure*Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Base Thickness/Radius to Center Line of Arch)^2)/12)/Diameter)). To calculate Thrust at Crown of Arch Dam, you need Normal Radial Pressure (p), Radius to Center Line of Arch (r), Theta (θ), Base Thickness (T_b) & Diameter (D). With our tool, you need to enter the respective value for Normal Radial Pressure, Radius to Center Line of Arch, Theta, Base Thickness & Diameter 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 Thrust of Abutments?

In this formula, Thrust of Abutments uses Normal Radial Pressure, Radius to Center Line of Arch, Theta, Base Thickness & Diameter. We can use 4 other way(s) to calculate the same, which is/are as follows -

Thrust of Abutments = Moment acting on Arch Dam/(Radius to Center Line of Arch*(sin(Theta)/(Theta-(cos(Theta)))))+Normal Radial Pressure*Radius to Center Line of Arch
Thrust of Abutments = Intrados Stresses*Base Thickness-6*Moment acting on Arch Dam/Base Thickness
Thrust of Abutments = Intrados Stresses*Base Thickness+6*Moment acting on Arch Dam/(Base Thickness^2)
Thrust of Abutments = Deflection due to Moments on Arch Dam*Elastic Modulus of Rock/Constant K2

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