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Rotation due to Moment on Arch Dam Formula

GoRotation due to Twist on Arch Dam Formula

GoRotation due to Shear on Arch Dam Formula

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Angle of Rotation is defined as by how many degrees the object is moved with respect to reference line. Check FAQs

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

Φ - Angle of Rotation?M_t - Moment acting on Arch Dam?K₁ - Constant K1?E - Elastic Modulus of Rock?t - Horizontal Thickness of an Arch?

Rotation due to Moment on Arch Dam Example

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Here is how the Rotation due to Moment on Arch Dam equation looks like with Values.

Here is how the Rotation due to Moment on Arch Dam equation looks like with Units.

Here is how the Rotation due to Moment on Arch Dam equation looks like.

37.1422 = 54.5 \cdot \frac{10.01}{10.2 \cdot 1.2 \cdot 1.2}

37.1422rad = 54.5N*m \cdot \frac{10.01}{10.2N/m² \cdot 1.2m \cdot 1.2m}

37.1422 = 54.5 \cdot \frac{10.01}{10.2 \cdot 1.2 \cdot 1.2}

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Rotation due to Moment on Arch Dam Solution

Follow our step by step solution on how to calculate Rotation due to Moment on Arch Dam?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Φ = 54.5N*m \cdot \frac{10.01}{10.2N/m² \cdot 1.2m \cdot 1.2m}

Next Step Convert Units

∴

Φ = 54.5J \cdot \frac{10.01}{10.2Pa \cdot 1.2m \cdot 1.2m}

Next Step Prepare to Evaluate

∴

Φ = 54.5 \cdot \frac{10.01}{10.2 \cdot 1.2 \cdot 1.2}

Next Step Evaluate

∴

Φ = 37.1422249455338rad

LAST Step Rounding Answer

∴

Φ = 37.1422rad

Rotation due to Moment on Arch Dam Formula Elements

Variables

Angle of Rotation

Angle of Rotation is defined as by how many degrees the object is moved with respect to reference line.

Symbol: Φ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle of Rotation

Moment acting on Arch Dam

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.

Symbol: M_t

Measurement: EnergyUnit: N*m

Note: Value can be positive or negative.

Formulas to find Moment acting on Arch Dam

Constant K1

Constant K1 is defined as the constant depending on b/a ratio and Poisson ratio of an Arch Dam.

Symbol: K₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant K1

Elastic Modulus of Rock

Elastic Modulus of Rock is defined as the linear elastic deformation response of rock under deformation.

Symbol: E

Measurement: PressureUnit: N/m²

Note: Value can be positive or negative.

Formulas to find Elastic Modulus of Rock

Horizontal Thickness of an Arch

Horizontal Thickness of an Arch, also known as the arch thickness or arch rise, refers to the distance between the intrados and the extrados along the horizontal axis.

Symbol: t

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Horizontal Thickness of an Arch

Other Formulas to find Angle of Rotation

Go Rotation due to Twist on Arch Dam

Φ = M \cdot \frac{K 4}{E \cdot t^{2}}

Go Rotation due to Shear on Arch Dam

Φ = F s \cdot \frac{K 5}{E \cdot t}

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 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}})

How to Evaluate Rotation due to Moment on Arch Dam?

Rotation due to Moment on Arch Dam evaluator uses Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch) to evaluate the Angle of Rotation, Rotation due to Moment on Arch Dam formula is defined as angle by which dam is tend to rotation due applied moment. Angle of Rotation is denoted by Φ symbol.

How to evaluate Rotation due to Moment on Arch Dam using this online evaluator? To use this online evaluator for Rotation due to Moment on Arch Dam, enter Moment acting on Arch Dam (M_t), Constant K1 (K₁), Elastic Modulus of Rock (E) & Horizontal Thickness of an Arch (t) and hit the calculate button.

FAQs on Rotation due to Moment on Arch Dam

What is the formula to find Rotation due to Moment on Arch Dam?

The formula of Rotation due to Moment on Arch Dam is expressed as Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch). Here is an example- 37.14222 = 54.5*10.01/(10.2*1.2*1.2).

How to calculate Rotation due to Moment on Arch Dam?

With Moment acting on Arch Dam (M_t), Constant K1 (K₁), Elastic Modulus of Rock (E) & Horizontal Thickness of an Arch (t) we can find Rotation due to Moment on Arch Dam using the formula - Angle of Rotation = Moment acting on Arch Dam*Constant K1/(Elastic Modulus of Rock*Horizontal Thickness of an Arch*Horizontal Thickness of an Arch).

What are the other ways to Calculate Angle of Rotation?

Here are the different ways to Calculate Angle of Rotation-

Angle of Rotation=Cantilever Twisting Moment*Constant K4/(Elastic Modulus of Rock*Horizontal Thickness of an Arch^2)
Angle of Rotation=Shear Force*Constant K5/(Elastic Modulus of Rock*Horizontal Thickness of an Arch)

Can the Rotation due to Moment on Arch Dam be negative?

No, the Rotation due to Moment on Arch Dam, measured in Angle cannot be negative.

Which unit is used to measure Rotation due to Moment on Arch Dam?

Rotation due to Moment on Arch Dam is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Rotation due to Moment on Arch Dam can be measured.

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Rotation due to Moment on Arch Dam Formula

​GoRotation due to Twist on Arch Dam Formula

​GoRotation due to Shear on Arch Dam Formula

Rotation due to Moment on Arch Dam Example

Rotation due to Moment on Arch Dam Solution

Rotation due to Moment on Arch Dam Formula Elements

Other Formulas to find Angle of Rotation

Other formulas in Arch Dams category

How to Evaluate Rotation due to Moment on Arch Dam?

FAQs on Rotation due to Moment on Arch Dam

Variable Name

GoRotation due to Twist on Arch Dam Formula

GoRotation due to Shear on Arch Dam Formula