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Sum of Normal Component given Factor of Safety Formula

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Sum of All Normal Component in Soil Mechanics is the total normal stress acting on a soil mass due to various factors such as self-weight, external loads, and pore water pressure. Check FAQs

ΣF N = \frac{(f s \cdot F t) - (c u \cdot L')}{\tan (\frac{Φ i \cdot π}{180})}

ΣF_N - Sum of All Normal Component in Soil Mechanics?f_s - Factor of Safety?F_t - Sum of All Tangential Component in Soil Mechanics?c_u - Unit Cohesion?L^' - Length of Slip Arc?Φ_i - Angle of Internal Friction of Soil?π - Archimedes' constant?

Sum of Normal Component given Factor of Safety Example

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Here is how the Sum of Normal Component given Factor of Safety equation looks like with Values.

Here is how the Sum of Normal Component given Factor of Safety equation looks like with Units.

Here is how the Sum of Normal Component given Factor of Safety equation looks like.

31.6448 = \frac{(2.8 \cdot 11) - (10 \cdot 3.0001)}{\tan (\frac{82.87 \cdot 3.1416}{180})}

31.6448N = \frac{(2.8 \cdot 11N) - (10Pa \cdot 3.0001m)}{\tan (\frac{82.87° \cdot 3.1416}{180})}

31.6448 = \frac{(2.8 \cdot 11) - (10 \cdot 3.0001)}{\tan (\frac{82.87 \cdot 3.1416}{180})}

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Sum of Normal Component given Factor of Safety Solution

Follow our step by step solution on how to calculate Sum of Normal Component given Factor of Safety?

FIRST Step Consider the formula

ΣF N = \frac{(f s \cdot F t) - (c u \cdot L')}{\tan (\frac{Φ i \cdot π}{180})}

Next Step Substitute values of Variables

∴

ΣF N = \frac{(2.8 \cdot 11N) - (10Pa \cdot 3.0001m)}{\tan (\frac{82.87° \cdot π}{180})}

Next Step Substitute values of Constants

∴

ΣF N = \frac{(2.8 \cdot 11N) - (10Pa \cdot 3.0001m)}{\tan (\frac{82.87° \cdot 3.1416}{180})}

Next Step Convert Units

∴

ΣF N = \frac{(2.8 \cdot 11N) - (10Pa \cdot 3.0001m)}{\tan (\frac{1.4464rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

ΣF N = \frac{(2.8 \cdot 11) - (10 \cdot 3.0001)}{\tan (\frac{1.4464 \cdot 3.1416}{180})}

Next Step Evaluate

∴

ΣF N = 31.6448062796375N

LAST Step Rounding Answer

∴

ΣF N = 31.6448N

Sum of Normal Component given Factor of Safety Formula Elements

Variables

Constants

Functions

Sum of All Normal Component in Soil Mechanics

Sum of All Normal Component in Soil Mechanics is the total normal stress acting on a soil mass due to various factors such as self-weight, external loads, and pore water pressure.

Symbol: ΣF_N

Measurement: ForceUnit: N

Note: Value should be between 0 to 180.

Formulas to find Sum of All Normal Component in Soil Mechanics

Factor of Safety

Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

Sum of All Tangential Component in Soil Mechanics

Sum of All Tangential Component in Soil Mechanics means total tangential component.

Symbol: F_t

Measurement: ForceUnit: N

Note: Value should be between 0 to 180.

Formulas to find Sum of All Tangential Component in Soil Mechanics

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 Factor of Safety?

Sum of Normal Component given Factor of Safety evaluator uses Sum of All Normal Component in Soil Mechanics = ((Factor of Safety*Sum of All Tangential Component in Soil Mechanics)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction of Soil*pi)/180) to evaluate the Sum of All Normal Component in Soil Mechanics, The Sum of Normal Component given Factor of Safety formula is defined as the sum of forces acting perpendicular (normal) to the potential failure plane in the soil or rock mass. This component is crucial in determining the stability of slopes or retaining structures. Sum of All Normal Component in Soil Mechanics is denoted by ΣF_N symbol.

How to evaluate Sum of Normal Component given Factor of Safety using this online evaluator? To use this online evaluator for Sum of Normal Component given Factor of Safety, enter Factor of Safety (f_s), Sum of All Tangential Component in Soil Mechanics (F_t), 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 Factor of Safety

What is the formula to find Sum of Normal Component given Factor of Safety?

The formula of Sum of Normal Component given Factor of Safety is expressed as Sum of All Normal Component in Soil Mechanics = ((Factor of Safety*Sum of All Tangential Component in Soil Mechanics)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction of Soil*pi)/180). Here is an example- 483.1873 = ((2.8*11)-(10*3.0001))/tan((1.44635435112743*pi)/180).

How to calculate Sum of Normal Component given Factor of Safety?

With Factor of Safety (f_s), Sum of All Tangential Component in Soil Mechanics (F_t), 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 Factor of Safety using the formula - Sum of All Normal Component in Soil Mechanics = ((Factor of Safety*Sum of All Tangential Component in Soil Mechanics)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction of Soil*pi)/180). This formula also uses Archimedes' constant and Tangent (tan) function(s).

Can the Sum of Normal Component given Factor of Safety be negative?

Yes, the Sum of Normal Component given Factor of Safety, measured in Force can be negative.

Which unit is used to measure Sum of Normal Component given Factor of Safety?

Sum of Normal Component given Factor of Safety 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 Factor of Safety can be measured.

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Sum of Normal Component given Factor of Safety Formula

Sum of Normal Component given Factor of Safety Example

Sum of Normal Component given Factor of Safety Solution

Sum of Normal Component given Factor of Safety Formula Elements

Other formulas in The Swedish Slip Circle Method category

How to Evaluate Sum of Normal Component given Factor of Safety?

FAQs on Sum of Normal Component given Factor of Safety

Variable Name