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Radius to centerline given Thrust at Abutments of Arch Dam Formula

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

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

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

Radius to centerline given Thrust at Abutments of Arch Dam Example

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Here is how the Radius to centerline given Thrust at Abutments of Arch Dam equation looks like with Values.

Here is how the Radius to centerline given Thrust at Abutments of Arch Dam equation looks like with Units.

Here is how the Radius to centerline given Thrust at Abutments of Arch Dam equation looks like.

5.4846 = \frac{\frac{16 - 63.55 \cdot \cos (30)}{1 - \cos (30)}}{21.7}

5.4846m = \frac{\frac{16kN/m - 63.55N \cdot \cos (30°)}{1 - \cos (30°)}}{21.7kPa/m²}

5.4846 = \frac{\frac{16 - 63.55 \cdot \cos (30)}{1 - \cos (30)}}{21.7}

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Radius to centerline given Thrust at Abutments of Arch Dam Solution

Follow our step by step solution on how to calculate Radius to centerline given Thrust at Abutments of Arch Dam?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r = \frac{\frac{16kN/m - 63.55N \cdot \cos (30°)}{1 - \cos (30°)}}{21.7kPa/m²}

Next Step Convert Units

∴

r = \frac{\frac{16000N/m - 63.55N \cdot \cos (0.5236rad)}{1 - \cos (0.5236rad)}}{21700Pa/m²}

Next Step Prepare to Evaluate

∴

r = \frac{\frac{16000 - 63.55 \cdot \cos (0.5236)}{1 - \cos (0.5236)}}{21700}

Next Step Evaluate

∴

r = 5.48455447855125m

LAST Step Rounding Answer

∴

r = 5.4846m

Radius to centerline given Thrust at Abutments of Arch Dam Formula Elements

Variables

Functions

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 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

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

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

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

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 in Arch Dams category

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

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

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 Radius to centerline given Thrust at Abutments of Arch Dam?

Radius to centerline given Thrust at Abutments of Arch Dam evaluator uses Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure to evaluate 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 evaluate Radius to centerline given Thrust at Abutments of Arch Dam using this online evaluator? To use this online evaluator for Radius to centerline given Thrust at Abutments of Arch Dam, enter Thrust from Water (P), Thrust of Abutments (F), Theta (θ) & Radial Pressure (P_v) and hit the calculate button.

FAQs on Radius to centerline given Thrust at Abutments of Arch Dam

What is the formula to find Radius to centerline given Thrust at Abutments of Arch Dam?

The formula of Radius to centerline given Thrust at Abutments of Arch Dam is expressed as Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure. Here is an example- 5.950742 = ((16000-63.55*cos(0.5235987755982))/(1-cos(0.5235987755982)))/21700.

How to calculate Radius to centerline given Thrust at Abutments of Arch Dam?

With Thrust from Water (P), Thrust of Abutments (F), Theta (θ) & Radial Pressure (P_v) we can find Radius to centerline given Thrust at Abutments of Arch Dam using the formula - Radius to Center Line of Arch = ((Thrust from Water-Thrust of Abutments*cos(Theta))/(1-cos(Theta)))/Radial Pressure. This formula also uses Cosine (cos) function(s).

Can the Radius to centerline given Thrust at Abutments of Arch Dam be negative?

No, the Radius to centerline given Thrust at Abutments of Arch Dam, measured in Length cannot be negative.

Which unit is used to measure Radius to centerline given Thrust at Abutments of Arch Dam?

Radius to centerline given Thrust at Abutments of Arch Dam is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Radius to centerline given Thrust at Abutments of Arch Dam can be measured.

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Radius to centerline given Thrust at Abutments of Arch Dam Formula

Radius to centerline given Thrust at Abutments of Arch Dam Example

Radius to centerline given Thrust at Abutments of Arch Dam Solution

Radius to centerline given Thrust at Abutments of Arch Dam Formula Elements

Other formulas in Arch Dams category

How to Evaluate Radius to centerline given Thrust at Abutments of Arch Dam?

FAQs on Radius to centerline given Thrust at Abutments of Arch Dam

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