Thrust at Crown of Arch Dam given Moment at Abutments Calculator

✖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.ⓘ Moment acting on Arch Dam [M_t]			+10% -10%
✖Radius to Center Line of Arch is a radial line from the focus to any point of a curve.ⓘ Radius to Center Line of Arch [r]			+10% -10%
✖Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.ⓘ Theta [θ]			+10% -10%
✖Normal Radial Pressure at the center line is the extrados pressure times the ratio of the upstream radius to the center-line radius.ⓘ Normal Radial Pressure [p]			+10% -10%

✖Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.ⓘ Thrust at Crown of Arch Dam given Moment at Abutments [F]

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Thrust at Crown of Arch Dam given Moment at Abutments Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
F = M_t/(r*(sin(θ)/(θ-(cos(θ)))))+p*r
This formula uses 2 Functions, 5 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Thrust of Abutments - (Measured in Newton) - Thrust of Abutments refers to the horizontal force exerted by an arch, vault, or similar structure against its supporting abutments.
Moment acting on Arch Dam - (Measured in Joule) - 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.
Radius to Center Line of Arch - (Measured in Meter) - Radius to Center Line of Arch is a radial line from the focus to any point of a curve.
Theta - (Measured in Radian) - Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint.
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.

STEP 1: Convert Input(s) to Base Unit

Moment acting on Arch Dam: 54.5 Newton Meter --> 54.5 Joule (Check conversion here)
Radius to Center Line of Arch: 5.5 Meter --> 5.5 Meter No Conversion Required
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Normal Radial Pressure: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F = M_t/(r*(sin(θ)/(θ-(cos(θ)))))+p*r --> 54.5/(5.5*(sin(0.5235987755982)/(0.5235987755982-(cos(0.5235987755982)))))+8*5.5

Evaluating ... ...

F = 37.2137268232182

STEP 3: Convert Result to Output's Unit

37.2137268232182 Newton --> No Conversion Required

FINAL ANSWER

37.2137268232182 ≈ 37.21373 Newton <-- Thrust of Abutments

(Calculation completed in 00.004 seconds)

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< Thrust on Arch Dam Calculators

Thrust at Crown of Arch Dam given Moment at Abutments

LaTeX Go 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 at Crown of Arch Dam

LaTeX Go 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))

Thrust at Abutments of Arch Dam

LaTeX Go Thrust from Water = Radial Pressure*Radius to Center Line of Arch-(Radial Pressure*Radius to Center Line of Arch-Thrust of Abutments)*cos(Theta)

Thrust given Intrados Stresses on Arch Dam

LaTeX Go Thrust of Abutments = Intrados Stresses*Base Thickness-6*Moment acting on Arch Dam/Base Thickness

Thrust at Crown of Arch Dam given Moment at Abutments Formula

LaTeX Go

What are Abutments ?

An abutment is the substructure at the ends of a bridge span or dam supporting its superstructure. Single-span bridges have abutments at each end which provide vertical and lateral support for the span, as well as acting as retaining walls to resist lateral movement of the earthen fill of the bridge approach.

How to Calculate Thrust at Crown of Arch Dam given Moment at Abutments?

Thrust at Crown of Arch Dam given Moment at Abutments calculator uses 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 to calculate the Thrust of Abutments, The Thrust at Crown of Arch Dam given Moment at Abutments of Arch Damis the horizontal force exerted on the dam due to the water pressure, resisting the overturning moment generated by the water and preventing the dam from collapsing. Thrust of Abutments is denoted by F symbol.

How to calculate Thrust at Crown of Arch Dam given Moment at Abutments using this online calculator? To use this online calculator for Thrust at Crown of Arch Dam given Moment at Abutments, enter Moment acting on Arch Dam (M_t), Radius to Center Line of Arch (r), Theta (θ) & Normal Radial Pressure (p) and hit the calculate button. Here is how the Thrust at Crown of Arch Dam given Moment at Abutments calculation can be explained with given input values -> 37.21373 = 54.5/(5.5*(sin(0.5235987755982)/(0.5235987755982-(cos(0.5235987755982)))))+8*5.5.

FAQ

What is Thrust at Crown of Arch Dam given Moment at Abutments?

The Thrust at Crown of Arch Dam given Moment at Abutments of Arch Damis the horizontal force exerted on the dam due to the water pressure, resisting the overturning moment generated by the water and preventing the dam from collapsing and is represented as F = M_t/(r*(sin(θ)/(θ-(cos(θ)))))+p*r or 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. 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, Radius to Center Line of Arch is a radial line from the focus to any point of a curve, Theta is an angle that can be defined as the figure formed by two rays meeting at a common endpoint & Normal Radial Pressure at the center line is the extrados pressure times the ratio of the upstream radius to the center-line radius.

How to calculate Thrust at Crown of Arch Dam given Moment at Abutments?

The Thrust at Crown of Arch Dam given Moment at Abutments of Arch Damis the horizontal force exerted on the dam due to the water pressure, resisting the overturning moment generated by the water and preventing the dam from collapsing is calculated using 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. To calculate Thrust at Crown of Arch Dam given Moment at Abutments, you need Moment acting on Arch Dam (M_t), Radius to Center Line of Arch (r), Theta (θ) & Normal Radial Pressure (p). With our tool, you need to enter the respective value for Moment acting on Arch Dam, Radius to Center Line of Arch, Theta & Normal Radial Pressure and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Thrust of Abutments?

In this formula, Thrust of Abutments uses Moment acting on Arch Dam, Radius to Center Line of Arch, Theta & Normal Radial Pressure. We can use 3 other way(s) to calculate the same, which is/are as follows -

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))
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)

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