Factor of Safety given Sum of Tangential Component Calculator

✖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%
✖Sum of all Normal Component means total normal force on slip circle.ⓘ Sum of all Normal Component [ΣN]			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%
✖Sum of all Tangential Component means total tangential component.ⓘ Sum of all Tangential Component [ΣT]			+10% -10%

✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety given Sum of Tangential Component [f_s]

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Formula

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Factor of Safety given Sum of Tangential Component

Formula

`"f"_{"s"} = (("c"_{"u"}*"L"^{"'"})+("ΣN"*tan(("φ"*pi)/180)))/"ΣT"`

Example

`"6.014213"=(("10Pa"*"3.0001m")+("5N"*tan(("46°"*pi)/180)))/"5N"`

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Factor of Safety given Sum of Tangential Component Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor of Safety = ((Unit Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Angle of Internal Friction*pi)/180)))/Sum of all Tangential Component
f_s = ((c_u*L^')+(ΣN*tan((φ*pi)/180)))/ΣT
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

Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
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.
Sum of all Normal Component - (Measured in Newton) - Sum of all Normal Component means total normal force on slip circle.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .
Sum of all Tangential Component - (Measured in Newton) - Sum of all Tangential Component means total tangential component.

STEP 1: Convert Input(s) to Base Unit

Unit Cohesion: 10 Pascal --> 10 Pascal No Conversion Required
Length of Slip Arc: 3.0001 Meter --> 3.0001 Meter No Conversion Required
Sum of all Normal Component: 5 Newton --> 5 Newton No Conversion Required
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
Sum of all Tangential Component: 5 Newton --> 5 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = ((c_u*L^')+(ΣN*tan((φ*pi)/180)))/ΣT --> ((10*3.0001)+(5*tan((0.802851455917241*pi)/180)))/5

Evaluating ... ...

f_s = 6.0142133184817

STEP 3: Convert Result to Output's Unit

6.0142133184817 --> No Conversion Required

FINAL ANSWER

6.0142133184817 ≈ 6.014213 <-- Factor of Safety

(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 » Factor of Safety given Sum of Tangential Component

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Created by Suraj Kumar

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

Factor of Safety given Sum of Tangential Component Formula

What is Factor of Safety?

The factor of safety is the structural capacity of a system which determines the load-carrying capacity beyond its actual load. In other words, how strong the system is then what is actually required is called factor of safety.

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

Factor of Safety given Sum of Tangential Component calculator uses Factor of Safety = ((Unit Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Angle of Internal Friction*pi)/180)))/Sum of all Tangential Component to calculate the Factor of Safety, The Factor of Safety given Sum of Tangential Component is defined as the ratio of allowable stress to the sum of tangential components to ensure structural stability. Factor of Safety is denoted by f_s symbol.

How to calculate Factor of Safety given Sum of Tangential Component using this online calculator? To use this online calculator for Factor of Safety given Sum of Tangential Component, enter Unit Cohesion (c_u), Length of Slip Arc (L^'), Sum of all Normal Component (ΣN), Angle of Internal Friction (φ) & Sum of all Tangential Component (ΣT) and hit the calculate button. Here is how the Factor of Safety given Sum of Tangential Component calculation can be explained with given input values -> 6.014013 = ((10*3.0001)+(5*tan((0.802851455917241*pi)/180)))/5.

FAQ

What is Factor of Safety given Sum of Tangential Component?

The Factor of Safety given Sum of Tangential Component is defined as the ratio of allowable stress to the sum of tangential components to ensure structural stability and is represented as f_s = ((c_u*L^')+(ΣN*tan((φ*pi)/180)))/ΣT or Factor of Safety = ((Unit Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Angle of Internal Friction*pi)/180)))/Sum of all 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, Sum of all Normal Component means total normal force on slip circle, Angle of Internal Friction is the angle measured between the normal force and resultant force & Sum of all Tangential Component means total tangential component.

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

The Factor of Safety given Sum of Tangential Component is defined as the ratio of allowable stress to the sum of tangential components to ensure structural stability is calculated using Factor of Safety = ((Unit Cohesion*Length of Slip Arc)+(Sum of all Normal Component*tan((Angle of Internal Friction*pi)/180)))/Sum of all Tangential Component. To calculate Factor of Safety given Sum of Tangential Component, you need Unit Cohesion (c_u), Length of Slip Arc (L^'), Sum of all Normal Component (ΣN), Angle of Internal Friction (φ) & Sum of all Tangential Component (ΣT). With our tool, you need to enter the respective value for Unit Cohesion, Length of Slip Arc, Sum of all Normal Component, Angle of Internal Friction & Sum of all Tangential Component and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Factor of Safety?

In this formula, Factor of Safety uses Unit Cohesion, Length of Slip Arc, Sum of all Normal Component, Angle of Internal Friction & Sum of all Tangential Component. We can use 3 other way(s) to calculate the same, which is/are as follows -

Factor of Safety = Resisting Moment/Driving Moment
Factor of Safety = (Unit Cohesion*Length of Slip Arc*Radial Distance)/(Weight of Body in Newtons*Distance)
Factor of Safety = Unit Cohesion/Mobilised Shear Resistance of Soil

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