Radius to centerline 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%
✖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.ⓘ Theta [θ]			+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 centerline given Thrust at Abutments of Arch Dam [r]

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Radius to centerline given Thrust at Abutments of Arch Dam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure
r = ((P-F*cos(θ))/(1-cos(θ)))/P_v
This formula uses 1 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)

Variables Used

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 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.
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.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
Radial Pressure - (Measured in Pascal per Square Meter) - Radial pressure is a pressure towards or away from the central axis of a component.

STEP 1: Convert Input(s) to Base Unit

Thrust from Water: 16 Kilonewton per Meter --> 16000 Newton per Meter (Check conversion here)
Thrust of Abutments: 63.55 Newton --> 63.55 Newton No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Radial Pressure: 21.7 Kilopascal per Square Meter --> 21700 Pascal per Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = ((P-F*cos(θ))/(1-cos(θ)))/P_v --> ((16000-63.55*cos(0.5235987755982))/(1-cos(0.5235987755982)))/21700

Evaluating ... ...

r = 5.48455447855125

STEP 3: Convert Result to Output's Unit

5.48455447855125 Meter --> No Conversion Required

FINAL ANSWER

5.48455447855125 ≈ 5.484554 Meter <-- Radius to Center Line of Arch

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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))

Radius to centerline given Thrust at Abutments of Arch Dam Formula

LaTeX Go

Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure
r = ((P-F*cos(θ))/(1-cos(θ)))/P_v

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 Radius to centerline given Thrust at Abutments of Arch Dam?

Radius to centerline given Thrust at Abutments of Arch Dam calculator uses Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure to calculate the Radius to Center Line of Arch, Radius to centerline given Thrust at Abutments of Arch Dam is defined as total sectional plan of dam. Radius to Center Line of Arch is denoted by r symbol.

How to calculate Radius to centerline given Thrust at Abutments of Arch Dam using this online calculator? To use this online calculator for Radius to centerline given Thrust at Abutments of Arch Dam, enter Thrust from Water (P), Thrust of Abutments (F), Theta (θ) & Radial Pressure (P_v) and hit the calculate button. Here is how the Radius to centerline given Thrust at Abutments of Arch Dam calculation can be explained with given input values -> 5.950742 = ((16000-63.55*cos(0.5235987755982))/(1-cos(0.5235987755982)))/21700.

FAQ

What is Radius to centerline given Thrust at Abutments of Arch Dam?

Radius to centerline given Thrust at Abutments of Arch Dam is defined as total sectional plan of dam and is represented as r = ((P-F*cos(θ))/(1-cos(θ)))/P_v or Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure. Thrust from water retained behind a wall is the force applied by the water on unit length of wall, Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments, Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint & Radial pressure is a pressure towards or away from the central axis of a component.

How to calculate Radius to centerline given Thrust at Abutments of Arch Dam?

Radius to centerline given Thrust at Abutments of Arch Dam is defined as total sectional plan of dam is calculated using Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure. To calculate Radius to centerline given Thrust at Abutments of Arch Dam, you need Thrust from Water (P), Thrust of Abutments (F), Theta (θ) & Radial Pressure (P_v). With our tool, you need to enter the respective value for Thrust from Water, Thrust of Abutments, Theta & Radial Pressure 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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