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Thrust at Abutments of Arch Dam Formula

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

P = P v \cdot r - (P v \cdot r - F) \cdot \cos (θ)

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

Thrust at Abutments of Arch Dam Example

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

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

Here is how the Thrust at Abutments of Arch Dam equation looks like.

16.0449 = 21.7 \cdot 5.5 - (21.7 \cdot 5.5 - 63.55) \cdot \cos (30)

16.0449kN/m = 21.7kPa/m² \cdot 5.5m - (21.7kPa/m² \cdot 5.5m - 63.55N) \cdot \cos (30°)

16.0449 = 21.7 \cdot 5.5 - (21.7 \cdot 5.5 - 63.55) \cdot \cos (30)

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Thrust at Abutments of Arch Dam Solution

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

FIRST Step Consider the formula

P = P v \cdot r - (P v \cdot r - F) \cdot \cos (θ)

Next Step Substitute values of Variables

∴

P = 21.7kPa/m² \cdot 5.5m - (21.7kPa/m² \cdot 5.5m - 63.55N) \cdot \cos (30°)

Next Step Convert Units

∴

P = 21700Pa/m² \cdot 5.5m - (21700Pa/m² \cdot 5.5m - 63.55N) \cdot \cos (0.5236rad)

Next Step Prepare to Evaluate

∴

P = 21700 \cdot 5.5 - (21700 \cdot 5.5 - 63.55) \cdot \cos (0.5236)

Next Step Evaluate

∴

P = 16044.9039727378N/m

Next Step Convert to Output's Unit

∴

P = 16.0449039727378kN/m

LAST Step Rounding Answer

∴

P = 16.0449kN/m

Thrust at Abutments of Arch Dam Formula Elements

Variables

Functions

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

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

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 Thrust on Arch Dam category

Go Thrust at Crown of Arch Dam

F = (p \cdot r) \cdot (1 - (2 \cdot θ \cdot \frac{\sin (θ \cdot \frac{{(\frac{T b}{r})}^{2}}{12})}{D}))

Go Thrust at Crown of Arch Dam given Moment at Abutments

F = \frac{M t}{r \cdot (\frac{\sin (θ)}{θ - (\cos (θ))})} + p \cdot r

Go Thrust given Intrados Stresses on Arch Dam

F = S \cdot T b - 6 \cdot \frac{M t}{T b}

Go Thrust given Extrados Stresses on Arch Dam

F = S \cdot T b + 6 \cdot \frac{M t}{{T b}^{2}}

How to Evaluate Thrust at Abutments of Arch Dam?

Thrust at Abutments of Arch Dam evaluator uses Thrust from Water = Radial Pressure*Radius to Center Line of Arch-(Radial Pressure*Radius to Center Line of Arch-Thrust of Abutments)*cos(Theta) to evaluate the Thrust from Water, The Thrust at Abutments of Arch Dam formula is defined as normal upward force at abutments or side most point of dam. Thrust from Water is denoted by P symbol.

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

FAQs on Thrust at Abutments of Arch Dam

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

The formula of Thrust at Abutments of Arch Dam is expressed as Thrust from Water = Radial Pressure*Radius to Center Line of Arch-(Radial Pressure*Radius to Center Line of Arch-Thrust of Abutments)*cos(Theta). Here is an example- 0.014792 = 21700*5.5-(21700*5.5-63.55)*cos(0.5235987755982).

How to calculate Thrust at Abutments of Arch Dam?

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

Can the Thrust at Abutments of Arch Dam be negative?

No, the Thrust at Abutments of Arch Dam, measured in Surface Tension cannot be negative.

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

Thrust at Abutments of Arch Dam is usually measured using the Kilonewton per Meter[kN/m] for Surface Tension. Newton per Meter[kN/m], Millinewton per Meter[kN/m], Gram-Force per Centimeter[kN/m] are the few other units in which Thrust at Abutments of Arch Dam can be measured.

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Thrust at Abutments of Arch Dam Formula

Thrust at Abutments of Arch Dam Example

Thrust at Abutments of Arch Dam Solution

Thrust at Abutments of Arch Dam Formula Elements

Other formulas in Thrust on Arch Dam category

How to Evaluate Thrust at Abutments of Arch Dam?

FAQs on Thrust at Abutments of Arch Dam

Variable Name