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

✖Thrust from water retained behind a wall is the force applied by the water on unit length of wall.ⓘ Thrust from Water [P]			+10% -10%
✖Radial pressure is a pressure towards or away from the central axis of a component.ⓘ Radial Pressure [P_v]			+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%
✖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%

✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Angle between Crown and Abutments given Thrust at Abutments of Arch Dam [θ]

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

STEP 0: Pre-Calculation Summary

Formula Used

Theta = acos((Thrust from Water-Radial Pressure*Radius to Center Line of Arch)/(-Radial Pressure*Radius to Center Line of Arch+Thrust of Abutments))
θ = acos((P-P_v*r)/(-P_v*r+F))
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
Thrust from Water - (Measured in Newton per Meter) - Thrust from water retained behind a wall is the force applied by the water on unit length of wall.
Radial Pressure - (Measured in Pascal per Square Meter) - Radial pressure is a pressure towards or away from the central axis of a component.
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.
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

Thrust from Water: 16 Kilonewton per Meter --> 16000 Newton per Meter (Check conversion here)
Radial Pressure: 21.7 Kilopascal per Square Meter --> 21700 Pascal per Square Meter (Check conversion here)
Radius to Center Line of Arch: 5.5 Meter --> 5.5 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

θ = acos((P-P_v*r)/(-P_v*r+F)) --> acos((16000-21700*5.5)/(-21700*5.5+63.55))

Evaluating ... ...

θ = 0.522845407666328

STEP 3: Convert Result to Output's Unit

0.522845407666328 Radian -->29.9568351970832 Degree (Check conversion here)

FINAL ANSWER

29.9568351970832 ≈ 29.95684 Degree <-- Theta

(Calculation completed in 00.004 seconds)

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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))

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

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))
θ = acos((P-P_v*r)/(-P_v*r+F))

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

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam calculator uses Theta = acos((Thrust from Water-Radial Pressure*Radius to Center Line of Arch)/(-Radial Pressure*Radius to Center Line of Arch+Thrust of Abutments)) to calculate the Theta, The Angle between Crown and Abutments given Thrust at Abutments of Arch Dam formula is defined as side angle between the crown top and abutments. Theta is denoted by θ symbol.

How to calculate Angle between Crown and Abutments given Thrust at Abutments of Arch Dam using this online calculator? To use this online calculator for Angle between Crown and Abutments given Thrust at Abutments of Arch Dam, enter Thrust from Water (P), Radial Pressure (P_v), Radius to Center Line of Arch (r) & Thrust of Abutments (F) and hit the calculate button. Here is how the Angle between Crown and Abutments given Thrust at Abutments of Arch Dam calculation can be explained with given input values -> 1789.686 = acos((16000-21700*5.5)/(-21700*5.5+63.55)).

FAQ

What is Angle between Crown and Abutments given Thrust at Abutments of Arch Dam?

The Angle between Crown and Abutments given Thrust at Abutments of Arch Dam formula is defined as side angle between the crown top and abutments and is represented as θ = acos((P-P_v*r)/(-P_v*r+F)) or Theta = acos((Thrust from Water-Radial Pressure*Radius to Center Line of Arch)/(-Radial Pressure*Radius to Center Line of Arch+Thrust of Abutments)). Thrust from water retained behind a wall is the force applied by the water on unit length of wall, Radial pressure is a pressure towards or away from the central axis of a component, Radius to Center Line of Arch is a radial line from the focus to any point of a curve & Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.

How to calculate Angle between Crown and Abutments given Thrust at Abutments of Arch Dam?

The Angle between Crown and Abutments given Thrust at Abutments of Arch Dam formula is defined as side angle between the crown top and abutments is calculated using Theta = acos((Thrust from Water-Radial Pressure*Radius to Center Line of Arch)/(-Radial Pressure*Radius to Center Line of Arch+Thrust of Abutments)). To calculate Angle between Crown and Abutments given Thrust at Abutments of Arch Dam, you need Thrust from Water (P), Radial Pressure (P_v), Radius to Center Line of Arch (r) & Thrust of Abutments (F). With our tool, you need to enter the respective value for Thrust from Water, Radial Pressure, Radius to Center Line of 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.

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