Normal Radial Pressure at centerline given Moment at Crown of Arch Dam Calculator

✖Thrust at Crown refers to the force exerted horizontally against the dam structure at its highest point or crest.ⓘ Thrust at Crown [F_C]			+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%
✖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 acting on Arch Dam [M_t]			+10% -10%

✖Radial pressure is a pressure towards or away from the central axis of a component.ⓘ Normal Radial Pressure at centerline given Moment at Crown of Arch Dam [P_v]

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Formula

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Normal Radial Pressure at centerline given Moment at Crown of Arch Dam

Formula

`"P"_{"v"} = ("F"_{"C"}*"r"*(1-(sin("θ")/("θ")))-("M"_{"t"}))/(("r"^2)*(1-(sin("θ")/("θ")))) `

Example

`"21.77821kPa/m²"=("120kN"*"5.5m"*(1-(sin("30°")/("30°")))-("54.5N*m"))/((("5.5m")^2)*(1-(sin("30°")/("30°")))) `

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Normal Radial Pressure at centerline given Moment at Crown of Arch Dam Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*(1-(sin(Theta)/(Theta)))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*(1-(sin(Theta)/(Theta))))
P_v = (F_C*r*(1-(sin(θ)/(θ)))-(M_t))/((r^2)*(1-(sin(θ)/(θ))))
This formula uses 1 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)

Variables Used

Radial Pressure - (Measured in Pascal per Square Meter) - Radial pressure is a pressure towards or away from the central axis of a component.
Thrust at Crown - (Measured in Newton) - Thrust at Crown refers to the force exerted horizontally against the dam structure at its highest point or crest.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Thrust at Crown: 120 Kilonewton --> 120000 Newton (Check conversion here)
Radius to Center Line of Arch: 5.5 Meter --> 5.5 Meter No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Moment acting on Arch Dam: 54.5 Newton Meter --> 54.5 Joule (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_v = (F_C*r*(1-(sin(θ)/(θ)))-(M_t))/((r^2)*(1-(sin(θ)/(θ)))) --> (120000*5.5*(1-(sin(0.5235987755982)/(0.5235987755982)))-(54.5))/((5.5^2)*(1-(sin(0.5235987755982)/(0.5235987755982))))

Evaluating ... ...

P_v = 21778.2075727099

STEP 3: Convert Result to Output's Unit

21778.2075727099 Pascal per Square Meter -->21.7782075727099 Kilopascal per Square Meter (Check conversion here)

FINAL ANSWER

21.7782075727099 ≈ 21.77821 Kilopascal per Square Meter <-- Radial Pressure

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Dams » Arch Dams » Normal Radial Pressure of Arch Dams » Normal Radial Pressure at centerline given Moment at Crown of Arch Dam

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National Institute of Technology Karnataka (NITK), Surathkal

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< 4 Normal Radial Pressure of Arch Dams Calculators

Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam

Go Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*((sin(Theta)/(Theta))-cos(Theta))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*((sin(Theta)/(Theta))-cos(Theta)))

Normal Radial Pressure at centerline given Moment at Crown of Arch Dam

Go Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*(1-(sin(Theta)/(Theta)))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*(1-(sin(Theta)/(Theta))))

Normal Radial Pressure at centerline given Thrust at Crown of Arch Dam

Go Radial Pressure = Thrust at Crown/((Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Horizontal Thickness of an Arch/Radius to Center Line of Arch)^2)/12)/Diameter)))

Normal Radial Pressure at centerline given Thrust at Abutments of Arch Dam

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

Normal Radial Pressure at centerline given Moment 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 Normal Radial Pressure at centerline given Moment at Crown of Arch Dam?

Normal Radial Pressure at centerline given Moment at Crown of Arch Dam calculator uses Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*(1-(sin(Theta)/(Theta)))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*(1-(sin(Theta)/(Theta)))) to calculate the Radial Pressure, Normal Radial Pressure at centerline given Moment at Crown of Arch Dam is defined as pressure exerted due to water on dam. Radial Pressure is denoted by P_v symbol.

How to calculate Normal Radial Pressure at centerline given Moment at Crown of Arch Dam using this online calculator? To use this online calculator for Normal Radial Pressure at centerline given Moment at Crown of Arch Dam, enter Thrust at Crown (F_C), Radius to Center Line of Arch (r), Theta (θ) & Moment acting on Arch Dam (M_t) and hit the calculate button. Here is how the Normal Radial Pressure at centerline given Moment at Crown of Arch Dam calculation can be explained with given input values -> 0.021778 = (120000*5.5*(1-(sin(0.5235987755982)/(0.5235987755982)))-(54.5))/((5.5^2)*(1-(sin(0.5235987755982)/(0.5235987755982)))) .

FAQ

What is Normal Radial Pressure at centerline given Moment at Crown of Arch Dam?

Normal Radial Pressure at centerline given Moment at Crown of Arch Dam is defined as pressure exerted due to water on dam and is represented as P_v = (F_C*r*(1-(sin(θ)/(θ)))-(M_t))/((r^2)*(1-(sin(θ)/(θ)))) or Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*(1-(sin(Theta)/(Theta)))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*(1-(sin(Theta)/(Theta)))). Thrust at Crown refers to the force exerted horizontally against the dam structure at its highest point or crest, 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 & 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.

How to calculate Normal Radial Pressure at centerline given Moment at Crown of Arch Dam?

Normal Radial Pressure at centerline given Moment at Crown of Arch Dam is defined as pressure exerted due to water on dam is calculated using Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*(1-(sin(Theta)/(Theta)))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*(1-(sin(Theta)/(Theta)))). To calculate Normal Radial Pressure at centerline given Moment at Crown of Arch Dam, you need Thrust at Crown (F_C), Radius to Center Line of Arch (r), Theta (θ) & Moment acting on Arch Dam (M_t). With our tool, you need to enter the respective value for Thrust at Crown, Radius to Center Line of Arch, Theta & Moment acting on Arch Dam 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 Radial Pressure?

In this formula, Radial Pressure uses Thrust at Crown, Radius to Center Line of Arch, Theta & Moment acting on Arch Dam. We can use 3 other way(s) to calculate the same, which is/are as follows -

Radial Pressure = Thrust at Crown/((Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Horizontal Thickness of an Arch/Radius to Center Line of Arch)^2)/12)/Diameter)))
Radial Pressure = ((Thrust from Water+Thrust of Abutments*cos(Theta))/(Radius to Center Line of Arch-(Radius to Center Line of Arch*cos(Theta))))
Radial Pressure = (Thrust at Crown*Radius to Center Line of Arch*((sin(Theta)/(Theta))-cos(Theta))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*((sin(Theta)/(Theta))-cos(Theta)))

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