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Angle of Internal Friction given Resisting Moment Formula

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Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction. Check FAQs

Φ i = a \tan (\frac{(\frac{M R}{r}) - (c u \cdot L')}{ΣN})

Φ_i - Angle of Internal Friction of Soil?M_R - Resisting Moment?r - Radius of Slip Circle?c_u - Unit Cohesion?L^' - Length of Slip Arc?ΣN - Sum of all Normal Component?

Angle of Internal Friction given Resisting Moment Example

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Here is how the Angle of Internal Friction given Resisting Moment equation looks like with Values.

Here is how the Angle of Internal Friction given Resisting Moment equation looks like with Units.

Here is how the Angle of Internal Friction given Resisting Moment equation looks like.

89.9962 = a \tan (\frac{(\frac{45.05}{0.6}) - (10 \cdot 3.0001)}{5.01})

89.9962° = a \tan (\frac{(\frac{45.05kN*m}{0.6m}) - (10Pa \cdot 3.0001m)}{5.01N})

89.9962 = a \tan (\frac{(\frac{45.05}{0.6}) - (10 \cdot 3.0001)}{5.01})

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Angle of Internal Friction given Resisting Moment Solution

Follow our step by step solution on how to calculate Angle of Internal Friction given Resisting Moment?

FIRST Step Consider the formula

Φ i = a \tan (\frac{(\frac{M R}{r}) - (c u \cdot L')}{ΣN})

Next Step Substitute values of Variables

∴

Φ i = a \tan (\frac{(\frac{45.05kN*m}{0.6m}) - (10Pa \cdot 3.0001m)}{5.01N})

Next Step Convert Units

∴

Φ i = a \tan (\frac{(\frac{45050N*m}{0.6m}) - (10Pa \cdot 3.0001m)}{5.01N})

Next Step Prepare to Evaluate

∴

Φ i = a \tan (\frac{(\frac{45050}{0.6}) - (10 \cdot 3.0001)}{5.01})

Next Step Evaluate

∴

Φ i = 1.57072957426257rad

Next Step Convert to Output's Unit

∴

Φ i = 89.996175361643°

LAST Step Rounding Answer

∴

Φ i = 89.9962°

Angle of Internal Friction given Resisting Moment Formula Elements

Variables

Functions

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction.

Symbol: Φ_i

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Angle of Internal Friction of Soil

Open Variable

Resisting Moment

Resisting Moment is the moment (or torque) that counteracts the applied moment or load that tends to cause rotation or failure in a soil mass or structure.

Symbol: M_R

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Resisting Moment

Open Variable

Radius of Slip Circle

Radius of Slip Circle is the distance between center and one point on slip circle.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Slip Circle

Open Variable

Unit Cohesion

Unit Cohesion is the shear strength property of a soil that is solely attributed to cohesive forces between soil particles.

Symbol: c_u

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Unit Cohesion

Open Variable

Length of Slip Arc

Length of Slip Arc is the length of the arc formed by slip circle.

Symbol: L^'

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Slip Arc

Open Variable

Sum of all Normal Component

Sum of all Normal Component means total normal force on slip circle.

Symbol: ΣN

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Sum of all Normal Component

Open Variable

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

Other formulas in The Swedish Slip Circle Method category

Go Radial Distance from Center of Rotation given Length of Slip Arc

d radial = \frac{360 \cdot L'}{2 \cdot π \cdot δ \cdot (\frac{180}{π})}

Go Arc Angle given Length of Slip Arc

δ = \frac{360 \cdot L'}{2 \cdot π \cdot d radial} \cdot (\frac{π}{180})

Go Moment of Resistance given Factor of Safety

M r' = f s \cdot M D

Go Driving Moment given Factor of Safety

M D = \frac{M R}{f s}

See More

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How to Evaluate Angle of Internal Friction given Resisting Moment?

Angle of Internal Friction given Resisting Moment evaluator uses Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component) to evaluate the Angle of Internal Friction of Soil, The Angle of Internal Friction given Resisting Moment formula is defined as the angle at which a material's resisting moment equals the applied moment, stabilizing movement. Angle of Internal Friction of Soil is denoted by Φ_i symbol.

How to evaluate Angle of Internal Friction given Resisting Moment using this online evaluator? To use this online evaluator for Angle of Internal Friction given Resisting Moment, enter Resisting Moment (M_R), Radius of Slip Circle (r), Unit Cohesion (c_u), Length of Slip Arc (L^') & Sum of all Normal Component (ΣN) and hit the calculate button.

FAQs on Angle of Internal Friction given Resisting Moment

What is the formula to find Angle of Internal Friction given Resisting Moment?

The formula of Angle of Internal Friction given Resisting Moment is expressed as Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component). Here is an example- 5156.126 = atan(((45050/0.6)-(10*3.0001))/5.01).

How to calculate Angle of Internal Friction given Resisting Moment?

With Resisting Moment (M_R), Radius of Slip Circle (r), Unit Cohesion (c_u), Length of Slip Arc (L^') & Sum of all Normal Component (ΣN) we can find Angle of Internal Friction given Resisting Moment using the formula - Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

Can the Angle of Internal Friction given Resisting Moment be negative?

Yes, the Angle of Internal Friction given Resisting Moment, measured in Angle can be negative.

Which unit is used to measure Angle of Internal Friction given Resisting Moment?

Angle of Internal Friction given Resisting Moment is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Internal Friction given Resisting Moment can be measured.

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