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)))/Pv
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)))/Pv --> ((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 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal
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9 Arch Dams Calculators

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam
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
Go Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure
Rotation due to Moment on Arch Dam
Go Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch)
Intrados Stresses on Arch Dam
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
Go Intrados Stresses = (Thrust of Abutments/Horizontal Thickness of an Arch)-(6*Moment acting on Arch Dam/(Horizontal Thickness of an Arch^2))
Rotation due to Twist on Arch Dam
Go Angle of Rotation = Cantilever Twisting Moment*Constant K4/(Elastic Modulus of Rock*Horizontal Thickness of an Arch^2)
Shear Force given Rotation due to Shear on Arch Dam
Go Shear Force = Angle of Rotation*(Elastic Modulus of Rock*Horizontal Thickness of an Arch)/Constant K5
Rotation due to Shear on Arch Dam
Go Angle of Rotation = Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch)
Shear Force given Deflection due to Shear on Arch Dam
Go Shear Force = Deflection due to Moments on Arch Dam*Elastic Modulus of Rock/Constant K3

Radius to centerline given Thrust at Abutments of Arch Dam Formula

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)))/Pv

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 (Pv) 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)))/Pv 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 (Pv). 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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