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

GoNormal Radial Pressure at centerline given Thrust at Crown of Arch Dam Formula

GoNormal Radial Pressure at centerline given Moment at Crown of Arch Dam Formula

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Radial pressure is a pressure towards or away from the central axis of a component. Check FAQs

P v = \frac{F C \cdot r \cdot ((\frac{\sin (θ)}{θ}) - \cos (θ)) - (M t)}{(r^{2}) \cdot ((\frac{\sin (θ)}{θ}) - \cos (θ))}

P_v - Radial Pressure?F_C - Thrust at Crown?r - Radius to Center Line of Arch?θ - Theta?M_t - Moment acting on Arch Dam?

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

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Here is how the Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam equation looks like with Values.

Here is how the Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam equation looks like with Units.

Here is how the Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam equation looks like.

21.7979 = \frac{120 \cdot 5.5 \cdot ((\frac{\sin (30)}{30}) - \cos (30)) - (54.5)}{({5.5}^{2}) \cdot ((\frac{\sin (30)}{30}) - \cos (30))}

21.7979kPa/m² = \frac{120kN \cdot 5.5m \cdot ((\frac{\sin (30°)}{30°}) - \cos (30°)) - (54.5N*m)}{({5.5m}^{2}) \cdot ((\frac{\sin (30°)}{30°}) - \cos (30°))}

21.7979 = \frac{120 \cdot 5.5 \cdot ((\frac{\sin (30)}{30}) - \cos (30)) - (54.5)}{({5.5}^{2}) \cdot ((\frac{\sin (30)}{30}) - \cos (30))}

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

Follow our step by step solution on how to calculate Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam?

FIRST Step Consider the formula

P v = \frac{F C \cdot r \cdot ((\frac{\sin (θ)}{θ}) - \cos (θ)) - (M t)}{(r^{2}) \cdot ((\frac{\sin (θ)}{θ}) - \cos (θ))}

Next Step Substitute values of Variables

∴

P v = \frac{120kN \cdot 5.5m \cdot ((\frac{\sin (30°)}{30°}) - \cos (30°)) - (54.5N*m)}{({5.5m}^{2}) \cdot ((\frac{\sin (30°)}{30°}) - \cos (30°))}

Next Step Convert Units

∴

P v = \frac{120000N \cdot 5.5m \cdot ((\frac{\sin (0.5236rad)}{0.5236rad}) - \cos (0.5236rad)) - (54.5J)}{({5.5m}^{2}) \cdot ((\frac{\sin (0.5236rad)}{0.5236rad}) - \cos (0.5236rad))}

Next Step Prepare to Evaluate

∴

P v = \frac{120000 \cdot 5.5 \cdot ((\frac{\sin (0.5236)}{0.5236}) - \cos (0.5236)) - (54.5)}{({5.5}^{2}) \cdot ((\frac{\sin (0.5236)}{0.5236}) - \cos (0.5236))}

Next Step Evaluate

∴

P v = 21797.9167262885Pa/m²

Next Step Convert to Output's Unit

∴

P v = 21.7979167262885kPa/m²

LAST Step Rounding Answer

∴

P v = 21.7979kPa/m²

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

Variables

Functions

Radial Pressure

Radial pressure is a pressure towards or away from the central axis of a component.

Symbol: P_v

Measurement: Radial PressureUnit: kPa/m²

Note: Value can be positive or negative.

Formulas to find Radial Pressure

Thrust at Crown

Thrust at Crown refers to the force exerted horizontally against the dam structure at its highest point or crest.

Symbol: F_C

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Thrust at Crown

Radius to Center Line of Arch

Radius to Center Line of Arch is a radial line from the focus to any point of a curve.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius to Center Line of Arch

Theta

Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Theta

Moment acting on Arch Dam

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.

Symbol: M_t

Measurement: EnergyUnit: N*m

Note: Value can be positive or negative.

Formulas to find Moment acting on Arch Dam

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Radial Pressure

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

P v = \frac{F C}{(r) \cdot (1 - (2 \cdot θ \cdot \frac{\sin (θ \cdot \frac{{(\frac{t}{r})}^{2}}{12})}{D}))}

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

P v = \frac{F C \cdot r \cdot (1 - (\frac{\sin (θ)}{θ})) - (M t)}{(r^{2}) \cdot (1 - (\frac{\sin (θ)}{θ}))}

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

P v = (\frac{P + F \cdot \cos (θ)}{r - (r \cdot \cos (θ))})

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

Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam evaluator 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 evaluate 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 evaluate Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam?

The formula of Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam is expressed as 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))). Here is an example- 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))).

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

With Thrust at Crown (F_C), Radius to Center Line of Arch (r), Theta (θ) & Moment acting on Arch Dam (M_t) we can find Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam using the formula - 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))). This formula also uses Sine (sin), Cosine (cos) function(s).

What are the other ways to Calculate Radial Pressure?

Here are the different ways to Calculate Radial Pressure-

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))))

Can the Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam be negative?

Yes, the Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam, measured in Radial Pressure can be negative.

Which unit is used to measure 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 usually measured using the Kilopascal per Square Meter[kPa/m²] for Radial Pressure. Pascal per Square Meter[kPa/m²], Millipascal per Square Meter[kPa/m²], Megapascal per Square Meter[kPa/m²] are the few other units in which Normal Radial Pressure at centerline given Moment at Abutments of Arch Dam can be measured.

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

​GoNormal Radial Pressure at centerline given Thrust at Crown of Arch Dam Formula

​GoNormal Radial Pressure at centerline given Moment at Crown of Arch Dam Formula

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

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

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

Other Formulas to find Radial Pressure

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

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

Variable Name

GoNormal Radial Pressure at centerline given Thrust at Crown of Arch Dam Formula

GoNormal Radial Pressure at centerline given Moment at Crown of Arch Dam Formula