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Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Formula

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

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

θ - Theta?P - Thrust from Water?P_v - Radial Pressure?r - Radius to Center Line of Arch?F - Thrust of Abutments?

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Example

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Here is how the Angle between Crown and Abutments given Thrust at Abutments of Arch Dam equation looks like with Values.

Here is how the Angle between Crown and Abutments given Thrust at Abutments of Arch Dam equation looks like with Units.

Here is how the Angle between Crown and Abutments given Thrust at Abutments of Arch Dam equation looks like.

29.9568 = a \cos (\frac{16 - 21.7 \cdot 5.5}{- 21.7 \cdot 5.5 + 63.55})

29.9568° = a \cos (\frac{16kN/m - 21.7kPa/m² \cdot 5.5m}{- 21.7kPa/m² \cdot 5.5m + 63.55N})

29.9568 = a \cos (\frac{16 - 21.7 \cdot 5.5}{- 21.7 \cdot 5.5 + 63.55})

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Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Solution

Follow our step by step solution on how to calculate Angle between Crown and Abutments given Thrust at Abutments of Arch Dam?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{16kN/m - 21.7kPa/m² \cdot 5.5m}{- 21.7kPa/m² \cdot 5.5m + 63.55N})

Next Step Convert Units

∴

θ = a \cos (\frac{16000N/m - 21700Pa/m² \cdot 5.5m}{- 21700Pa/m² \cdot 5.5m + 63.55N})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{16000 - 21700 \cdot 5.5}{- 21700 \cdot 5.5 + 63.55})

Next Step Evaluate

∴

θ = 0.522845407666328rad

Next Step Convert to Output's Unit

∴

θ = 29.9568351970832°

LAST Step Rounding Answer

∴

θ = 29.9568°

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Formula Elements

Variables

Functions

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

Thrust from Water

Thrust from water retained behind a wall is the force applied by the water on unit length of wall.

Symbol: P

Measurement: Surface TensionUnit: kN/m

Note: Value should be greater than 0.

Formulas to find Thrust from Water

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

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

Thrust of Abutments

Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.

Symbol: F

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Thrust of Abutments

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

Other formulas in Arch Dams category

Go Radius to centerline given Thrust at Abutments of Arch Dam

r = \frac{\frac{P - F \cdot \cos (θ)}{1 - \cos (θ)}}{P v}

Go Intrados Stresses on Arch Dam

S = (\frac{F}{t}) + (6 \cdot \frac{M t}{t^{2}})

Go Extrados Stresses on Arch Dam

S = (\frac{F}{t}) - (6 \cdot \frac{M t}{t^{2}})

Go Rotation due to Moment on Arch Dam

Φ = M t \cdot \frac{K 1}{E \cdot t \cdot t}

How to Evaluate Angle between Crown and Abutments given Thrust at Abutments of Arch Dam?

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam evaluator uses Theta = acos((Thrust from Water-Radial Pressure*Radius to Center Line of Arch)/(-Radial Pressure*Radius to Center Line of Arch+Thrust of Abutments)) to evaluate the Theta, The Angle between Crown and Abutments given Thrust at Abutments of Arch Dam formula is defined as side angle between the crown top and abutments. Theta is denoted by θ symbol.

How to evaluate Angle between Crown and Abutments given Thrust at Abutments of Arch Dam using this online evaluator? To use this online evaluator for Angle between Crown and Abutments given Thrust at Abutments of Arch Dam, enter Thrust from Water (P), Radial Pressure (P_v), Radius to Center Line of Arch (r) & Thrust of Abutments (F) and hit the calculate button.

FAQs on Angle between Crown and Abutments given Thrust at Abutments of Arch Dam

What is the formula to find Angle between Crown and Abutments given Thrust at Abutments of Arch Dam?

The formula of Angle between Crown and Abutments given Thrust at Abutments of Arch Dam is expressed as Theta = acos((Thrust from Water-Radial Pressure*Radius to Center Line of Arch)/(-Radial Pressure*Radius to Center Line of Arch+Thrust of Abutments)). Here is an example- 1789.686 = acos((16000-21700*5.5)/(-21700*5.5+63.55)).

How to calculate Angle between Crown and Abutments given Thrust at Abutments of Arch Dam?

With Thrust from Water (P), Radial Pressure (P_v), Radius to Center Line of Arch (r) & Thrust of Abutments (F) we can find Angle between Crown and Abutments given Thrust at Abutments of Arch Dam using the formula - Theta = acos((Thrust from Water-Radial Pressure*Radius to Center Line of Arch)/(-Radial Pressure*Radius to Center Line of Arch+Thrust of Abutments)). This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

Can the Angle between Crown and Abutments given Thrust at Abutments of Arch Dam be negative?

Yes, the Angle between Crown and Abutments given Thrust at Abutments of Arch Dam, measured in Angle can be negative.

Which unit is used to measure Angle between Crown and Abutments given Thrust at Abutments of Arch Dam?

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle between Crown and Abutments given Thrust at Abutments of Arch Dam can be measured.

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Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Formula

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Example

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Solution

Angle between Crown and Abutments given Thrust at Abutments of Arch Dam Formula Elements

Other formulas in Arch Dams category

How to Evaluate Angle between Crown and Abutments given Thrust at Abutments of Arch Dam?

FAQs on Angle between Crown and Abutments given Thrust at Abutments of Arch Dam

Variable Name