Normal Radial Pressure at centerline given Moment at Abutments 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 Abutments of Arch Dam [P_v]

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Formula

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

Formula

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

Example

`"21.79792kPa/m²"=("120kN"*"5.5m"*((sin("30°")/("30°"))-cos("30°"))-("54.5N*m"))/((("5.5m")^2)*((sin("30°")/("30°"))-cos("30°")))`

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
P_v = (F_C*r*((sin(θ)/(θ))-cos(θ))-(M_t))/((r^2)*((sin(θ)/(θ))-cos(θ)))
This formula uses 2 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)
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

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*((sin(θ)/(θ))-cos(θ))-(M_t))/((r^2)*((sin(θ)/(θ))-cos(θ))) --> (120000*5.5*((sin(0.5235987755982)/(0.5235987755982))-cos(0.5235987755982))-(54.5))/((5.5^2)*((sin(0.5235987755982)/(0.5235987755982))-cos(0.5235987755982)))

Evaluating ... ...

P_v = 21797.9167262885

STEP 3: Convert Result to Output's Unit

21797.9167262885 Pascal per Square Meter -->21.7979167262885 Kilopascal per Square Meter (Check conversion here)

FINAL ANSWER

21.7979167262885 ≈ 21.79792 Kilopascal per Square Meter <-- Radial Pressure

(Calculation completed in 00.004 seconds)

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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 Abutments of Arch Dam Formula

What are Abutments ?

An abutment is the substructure at the ends of a bridge span or dam supporting its superstructure. Single-span bridges have abutments at each end which provide vertical and lateral support for the span, as well as acting as retaining walls to resist lateral movement of the earthen fill of the bridge approach.

How to Calculate Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam?

Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam calculator uses 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))) to calculate the Radial Pressure, Normal Radial Pressure at centerline given Moment at Abutments 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 Abutments of Arch Dam using this online calculator? To use this online calculator for Normal Radial Pressure at centerline given Moment at Abutments 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 Abutments of Arch Dam calculation can be explained with given input values -> 0.021798 = (120000*5.5*((sin(0.5235987755982)/(0.5235987755982))-cos(0.5235987755982))-(54.5))/((5.5^2)*((sin(0.5235987755982)/(0.5235987755982))-cos(0.5235987755982))).

FAQ

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

Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam is defined as pressure exerted due to water on dam and is represented as P_v = (F_C*r*((sin(θ)/(θ))-cos(θ))-(M_t))/((r^2)*((sin(θ)/(θ))-cos(θ))) or 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))). 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 Abutments of Arch Dam?

Normal Radial Pressure at centerline given Moment at Abutments 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*((sin(Theta)/(Theta))-cos(Theta))-(Moment acting on Arch Dam))/((Radius to Center Line of Arch^2)*((sin(Theta)/(Theta))-cos(Theta))). To calculate Normal Radial Pressure at centerline given Moment at Abutments 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 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))))
Radial Pressure = ((Thrust from Water+Thrust of Abutments*cos(Theta))/(Radius to Center Line of Arch-(Radius to Center Line of Arch*cos(Theta))))

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