Sum of Normal Component given Factor of Safety Calculator

✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety [f_s]			+10% -10%
✖Sum of All Tangential Component in Soil Mechanics means total tangential component.ⓘ Sum of All Tangential Component in Soil Mechanics [F_t]			+10% -10%
✖Unit Cohesion is the force that holds together molecules or like particles within a soil.ⓘ Unit Cohesion [c_u]			+10% -10%
✖Length of Slip Arc is the length of the arc formed by slip circle.ⓘ Length of Slip Arc [L^']			+10% -10%
✖Angle of Internal Friction of Soil is a shear strength parameter of soils.ⓘ Angle of Internal Friction of Soil [Φ_i]			+10% -10%

✖Sum of All Normal Component in Soil Mechanics means total normal force on slip circle.ⓘ Sum of Normal Component given Factor of Safety [ΣF_N]

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Formula

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Sum of Normal Component given Factor of Safety

Formula

`"ΣF"_{"N"} = (("f"_{"s"}*"F"_{"t"})-("c"_{"u"}*"L"^{"'"}))/tan(("Φ"_{"i"}*pi)/180)`

Example

`"31.64481N"=(("2.8"*"11N")-("10Pa"*"3.0001m"))/tan(("82.87°"*pi)/180)`

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Sum of Normal Component given Factor of Safety Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
ΣF_N = ((f_s*F_t)-(c_u*L^'))/tan((Φ_i*pi)/180)
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., tan(Angle)

Variables Used

Sum of All Normal Component in Soil Mechanics - (Measured in Newton) - Sum of All Normal Component in Soil Mechanics means total normal force on slip circle.
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Sum of All Tangential Component in Soil Mechanics - (Measured in Newton) - Sum of All Tangential Component in Soil Mechanics means total tangential component.
Unit Cohesion - (Measured in Pascal) - Unit Cohesion is the force that holds together molecules or like particles within a soil.
Length of Slip Arc - (Measured in Meter) - Length of Slip Arc is the length of the arc formed by slip circle.
Angle of Internal Friction of Soil - (Measured in Radian) - Angle of Internal Friction of Soil is a shear strength parameter of soils.

STEP 1: Convert Input(s) to Base Unit

Factor of Safety: 2.8 --> No Conversion Required
Sum of All Tangential Component in Soil Mechanics: 11 Newton --> 11 Newton No Conversion Required
Unit Cohesion: 10 Pascal --> 10 Pascal No Conversion Required
Length of Slip Arc: 3.0001 Meter --> 3.0001 Meter No Conversion Required
Angle of Internal Friction of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΣF_N = ((f_s*F_t)-(c_u*L^'))/tan((Φ_i*pi)/180) --> ((2.8*11)-(10*3.0001))/tan((1.44635435112743*pi)/180)

Evaluating ... ...

ΣF_N = 31.6448062796375

STEP 3: Convert Result to Output's Unit

31.6448062796375 Newton --> No Conversion Required

FINAL ANSWER

31.6448062796375 ≈ 31.64481 Newton <-- Sum of All Normal Component in Soil Mechanics

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Stability of Slopes In Earthen Dams » The Swedish Slip Circle Method » Sum of Normal Component given Factor of Safety

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Birsa Institute of Technology (BIT), Sindri

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< 25 The Swedish Slip Circle Method Calculators

Sum of Normal Component given Factor of Safety

Go 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)

Length of Slip Circle given Sum of Tangential Component

Go Length of Slip Arc = ((Factor of Safety*Sum of all Tangential Component)-(Sum of all Normal Component*tan((Angle of Internal Friction*pi)/180)))/Unit Cohesion

Sum of Tangential Component given Factor of Safety

Go Sum of all Tangential Component = ((Unit Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Angle of Internal Friction*pi)/180)))/Factor of Safety

Total Length of Slip Circle given Resisting Moment

Go Length of Slip Arc = ((Resisting Moment/Radius of Slip Circle)-(Sum of all Normal Component*tan((Angle of Internal Friction))))/Unit Cohesion

Sum of Normal Component given Resisting Moment

Go Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction))

Resisting Moment given Radius of Slip Circle

Go Resisting Moment = Radius of Slip Circle*((Unit Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Angle of Internal Friction))))

Normal Component given Resisting Force from Coulomb's Equation

Go Normal Component of Force in Soil Mechanics = (Resisting force in Soil Mechanics-(Unit Cohesion*Curve Length))/tan((Angle of Internal Friction of Soil))

Resisting Force from Coulomb's Equation

Go Resisting Force = ((Unit Cohesion*Curve Length)+(Normal Component of Force*tan((Angle of Internal Friction))))

Curve Length of Each Slice given Resisting Force from Coulomb's Equation

Go Curve Length = (Resisting Force-(Normal Component of Force*tan((Angle of Internal Friction))))/Unit Cohesion

Radial Distance from Centre of Rotation given Factor of Safety

Go Radial Distance = Factor of Safety/((Unit Cohesion*Length of Slip Arc)/(Weight of Body in Newtons*Distance))

Distance between Line of Action of Weight and Line Passing through Center

Go Distance = (Unit Cohesion*Length of Slip Arc*Radial Distance)/(Weight of Body in Newtons*Factor of Safety)

Distance between Line of Action and Line Passing through Center given Mobilised Cohesion

Go Distance = Mobilised Shear Resistance of Soil/((Weight of Body in Newtons*Radial Distance)/Length of Slip Arc)

Radial Distance from Centre of Rotation given Mobilised Shear resistance of Soil

Go Radial Distance = Mobilised Shear Resistance of Soil/((Weight of Body in Newtons*Distance)/Length of Slip Arc)

Mobilised Shear resistance of Soil given Weight of Soil on Wedge

Go Mobilised Shear Resistance of Soil = (Weight of Body in Newtons*Distance*Radial Distance)/Length of Slip Arc

Radial Distance from Center of Rotation given Length of Slip Arc

Go Radial Distance = (360*Length of Slip Arc)/(2*pi*Arc Angle*(180/pi))

Arc Angle given Length of Slip Arc

Go Arc Angle = (360*Length of Slip Arc)/(2*pi*Radial Distance)*(pi/180)

Radial Distance from Centre of Rotation given Moment of Resistance

Go Radial Distance = Resisting Moment/(Unit Cohesion*Length of Slip Arc)

Moment of Resistance given Unit Cohesion

Go Resisting Moment = (Unit Cohesion*Length of Slip Arc*Radial Distance)

Sum of Tangential Component given Driving Moment

Go Sum of all Tangential Component = Driving Moment/Radius of Slip Circle

Driving Moment given Radius of Slip Circle

Go Driving Moment = Radius of Slip Circle*Sum of all Tangential Component

Mobilised Shear resistance of Soil given Factor of Safety

Go Mobilised Shear Resistance of Soil = Unit Cohesion/Factor of Safety

Distance between Line of Action and Line Passing through Center given Driving Moment

Go Distance = Driving Moment/Weight of Body in Newtons

Driving Moment given Weight of Soil on Wedge

Go Driving Moment = Weight of Body in Newtons*Distance

Moment of Resistance given Factor of Safety

Go Resisting Moment = Factor of Safety*Driving Moment

Driving Moment given Factor of Safety

Go Driving Moment = Resisting Moment/Factor of Safety

Sum of Normal Component given Factor of Safety Formula

What is Normal Stress?

A normal stress is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area. A normal stress will occur when a member is placed in tension or compression.

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

Sum of Normal Component given Factor of Safety calculator 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 calculate the Sum of All Normal Component in Soil Mechanics, The Sum of Normal Component given Factor of Safety is defined as the force capacity divided by the factor of safety in structural design. Sum of All Normal Component in Soil Mechanics is denoted by ΣF_N symbol.

How to calculate Sum of Normal Component given Factor of Safety using this online calculator? To use this online calculator 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. Here is how the Sum of Normal Component given Factor of Safety calculation can be explained with given input values -> 31.68441 = ((2.8*11)-(10*3.0001))/tan((1.44635435112743*pi)/180).

FAQ

What is Sum of Normal Component given Factor of Safety?

The Sum of Normal Component given Factor of Safety is defined as the force capacity divided by the factor of safety in structural design and is represented as ΣF_N = ((f_s*F_t)-(c_u*L^'))/tan((Φ_i*pi)/180) or 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). Factor of Safety expresses how much stronger a system is than it needs to be for an intended load, Sum of All Tangential Component in Soil Mechanics means total tangential component, Unit Cohesion is the force that holds together molecules or like particles within a soil, Length of Slip Arc is the length of the arc formed by slip circle & Angle of Internal Friction of Soil is a shear strength parameter of soils.

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

The Sum of Normal Component given Factor of Safety is defined as the force capacity divided by the factor of safety in structural design is calculated using 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 calculate Sum of Normal Component given Factor of Safety, you need 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). With our tool, you need to enter the respective value for Factor of Safety, Sum of All Tangential Component in Soil Mechanics, Unit Cohesion, Length of Slip Arc & Angle of Internal Friction of Soil and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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