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Sum of Normal Component given Resisting Moment Formula

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

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

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

Sum of Normal Component given Resisting Moment Example

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Here is how the Sum of Normal Component given Resisting Moment equation looks like with Values.

Here is how the Sum of Normal Component given Resisting Moment equation looks like with Units.

Here is how the Sum of Normal Component given Resisting Moment equation looks like.

5.6393 = \frac{(\frac{45.05}{0.6}) - (10 \cdot 3.0001)}{\tan ((82.87))}

5.6393N = \frac{(\frac{45.05kN*m}{0.6m}) - (10Pa \cdot 3.0001m)}{\tan ((82.87°))}

5.6393 = \frac{(\frac{45.05}{0.6}) - (10 \cdot 3.0001)}{\tan ((82.87))}

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Sum of Normal Component given Resisting Moment Solution

Follow our step by step solution on how to calculate Sum of Normal Component given Resisting Moment?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ΣN = \frac{(\frac{45.05kN*m}{0.6m}) - (10Pa \cdot 3.0001m)}{\tan ((82.87°))}

Next Step Convert Units

∴

ΣN = \frac{(\frac{45.05kN*m}{0.6m}) - (10Pa \cdot 3.0001m)}{\tan ((1.4464rad))}

Next Step Prepare to Evaluate

∴

ΣN = \frac{(\frac{45.05}{0.6}) - (10 \cdot 3.0001)}{\tan ((1.4464))}

Next Step Evaluate

∴

ΣN = 5.63927429235379N

LAST Step Rounding Answer

∴

ΣN = 5.6393N

Sum of Normal Component given Resisting Moment Formula Elements

Variables

Functions

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

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

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

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

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

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

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)

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}

How to Evaluate Sum of Normal Component given Resisting Moment?

Sum of Normal Component given Resisting Moment evaluator uses Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction of Soil)) to evaluate the Sum of all Normal Component, The Sum of Normal Component given Resisting Moment is defined as the sum of forces acting perpendicular (normal) to the potential failure plane in the soil or rock mass, considering resisting moment. Sum of all Normal Component is denoted by ΣN symbol.

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

FAQs on Sum of Normal Component given Resisting Moment

What is the formula to find Sum of Normal Component given Resisting Moment?

The formula of Sum of Normal Component given Resisting Moment is expressed as Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction of Soil)). Here is an example- 5.639274 = ((45050/0.6)-(10*3.0001))/tan((1.44635435112743)).

How to calculate Sum of Normal Component given Resisting Moment?

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

Can the Sum of Normal Component given Resisting Moment be negative?

No, the Sum of Normal Component given Resisting Moment, measured in Force cannot be negative.

Which unit is used to measure Sum of Normal Component given Resisting Moment?

Sum of Normal Component given Resisting Moment is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Sum of Normal Component given Resisting Moment can be measured.

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Sum of Normal Component given Resisting Moment Formula

Sum of Normal Component given Resisting Moment Example

Sum of Normal Component given Resisting Moment Solution

Sum of Normal Component given Resisting Moment Formula Elements

Other formulas in The Swedish Slip Circle Method category

How to Evaluate Sum of Normal Component given Resisting Moment?

FAQs on Sum of Normal Component given Resisting Moment

Variable Name