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Thrust at Crown of Arch Dam Formula

GoThrust at Crown of Arch Dam given Moment at Abutments Formula

GoThrust given Intrados Stresses on Arch Dam Formula

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

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

F - Thrust of Abutments?p - Normal Radial Pressure?r - Radius to Center Line of Arch?θ - Theta?T_b - Base Thickness?D - Diameter?

Thrust at Crown of Arch Dam Example

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

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

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

43.9888 = (8 \cdot 5.5) \cdot (1 - (2 \cdot 30 \cdot \frac{\sin (30 \cdot \frac{{(\frac{1.3}{5.5})}^{2}}{12})}{9.999}))

43.9888N = (8 \cdot 5.5m) \cdot (1 - (2 \cdot 30° \cdot \frac{\sin (30° \cdot \frac{{(\frac{1.3m}{5.5m})}^{2}}{12})}{9.999m}))

43.9888 = (8 \cdot 5.5) \cdot (1 - (2 \cdot 30 \cdot \frac{\sin (30 \cdot \frac{{(\frac{1.3}{5.5})}^{2}}{12})}{9.999}))

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Thrust at Crown of Arch Dam Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F = (8 \cdot 5.5m) \cdot (1 - (2 \cdot 30° \cdot \frac{\sin (30° \cdot \frac{{(\frac{1.3m}{5.5m})}^{2}}{12})}{9.999m}))

Next Step Convert Units

∴

F = (8 \cdot 5.5m) \cdot (1 - (2 \cdot 0.5236rad \cdot \frac{\sin (0.5236rad \cdot \frac{{(\frac{1.3m}{5.5m})}^{2}}{12})}{9.999m}))

Next Step Prepare to Evaluate

∴

F = (8 \cdot 5.5) \cdot (1 - (2 \cdot 0.5236 \cdot \frac{\sin (0.5236 \cdot \frac{{(\frac{1.3}{5.5})}^{2}}{12})}{9.999}))

Next Step Evaluate

∴

F = 43.9887668127631N

LAST Step Rounding Answer

∴

F = 43.9888N

Thrust at Crown of Arch Dam Formula Elements

Variables

Functions

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

Normal Radial Pressure

Normal Radial Pressure at the center line is the extrados pressure times the ratio of the upstream radius to the center-line radius.

Symbol: p

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Normal 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

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

Base Thickness

Base Thickness is the maximum thickness or width of a dam measured horizontally between upstream and downstream faces and normal to the axis or centerline crest of the dam.

Symbol: T_b

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Base Thickness

Diameter

Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter

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)

Other Formulas to find Thrust of Abutments

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}}

Go Thrust given Deflection due to Thrust on Arch Dam

F = δ \cdot \frac{E}{K 2}

Other formulas in Thrust on Arch Dam category

Go Thrust at Abutments of Arch Dam

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

How to Evaluate Thrust at Crown of Arch Dam?

Thrust at Crown of Arch Dam evaluator uses Thrust of Abutments = (Normal Radial Pressure*Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Base Thickness/Radius to Center Line of Arch)^2)/12)/Diameter)) to evaluate the Thrust of Abutments, The Thrust at Crown of Arch Dam is defined as the horizontal force exerted by the water pressure on the curved upstream face of an arch dam, acting perpendicular to the dam axis at its highest point. Thrust of Abutments is denoted by F symbol.

How to evaluate Thrust at Crown of Arch Dam using this online evaluator? To use this online evaluator for Thrust at Crown of Arch Dam, enter Normal Radial Pressure (p), Radius to Center Line of Arch (r), Theta (θ), Base Thickness (T_b) & Diameter (D) and hit the calculate button.

FAQs on Thrust at Crown of Arch Dam

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

The formula of Thrust at Crown of Arch Dam is expressed as Thrust of Abutments = (Normal Radial Pressure*Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Base Thickness/Radius to Center Line of Arch)^2)/12)/Diameter)). Here is an example- 43.98877 = (8*5.5)*(1-(2*0.5235987755982*sin(0.5235987755982*((1.3/5.5)^2)/12)/9.999)).

How to calculate Thrust at Crown of Arch Dam?

With Normal Radial Pressure (p), Radius to Center Line of Arch (r), Theta (θ), Base Thickness (T_b) & Diameter (D) we can find Thrust at Crown of Arch Dam using the formula - Thrust of Abutments = (Normal Radial Pressure*Radius to Center Line of Arch)*(1-(2*Theta*sin(Theta*((Base Thickness/Radius to Center Line of Arch)^2)/12)/Diameter)). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Thrust of Abutments?

Here are the different ways to Calculate Thrust of Abutments-

Thrust of Abutments=Moment acting on Arch Dam/(Radius to Center Line of Arch*(sin(Theta)/(Theta-(cos(Theta)))))+Normal Radial Pressure*Radius to Center Line of Arch
Thrust of Abutments=Intrados Stresses*Base Thickness-6*Moment acting on Arch Dam/Base Thickness
Thrust of Abutments=Intrados Stresses*Base Thickness+6*Moment acting on Arch Dam/(Base Thickness^2)

Can the Thrust at Crown of Arch Dam be negative?

Yes, the Thrust at Crown of Arch Dam, measured in Force can be negative.

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

Thrust at Crown of Arch Dam is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Thrust at Crown of Arch Dam can be measured.

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Thrust at Crown of Arch Dam Formula

​GoThrust at Crown of Arch Dam given Moment at Abutments Formula

​GoThrust given Intrados Stresses on Arch Dam Formula

Thrust at Crown of Arch Dam Example

Thrust at Crown of Arch Dam Solution

Thrust at Crown of Arch Dam Formula Elements

Other Formulas to find Thrust of Abutments

Other formulas in Thrust on Arch Dam category

How to Evaluate Thrust at Crown of Arch Dam?

FAQs on Thrust at Crown of Arch Dam

Variable Name

GoThrust at Crown of Arch Dam given Moment at Abutments Formula

GoThrust given Intrados Stresses on Arch Dam Formula