Sum of Tangential Component given Factor of Safety Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
ΣT = ((cu*L')+(ΣN*tan((φ*pi)/180)))/fs
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 Tangential Component - (Measured in Newton) - Sum of all Tangential Component 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.
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 .
Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
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)
Factor of Safety: 2.8 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΣT = ((cu*L')+(ΣN*tan((φ*pi)/180)))/fs --> ((10*3.0001)+(5*tan((0.802851455917241*pi)/180)))/2.8
Evaluating ... ...
ΣT = 10.7396666401459
STEP 3: Convert Result to Output's Unit
10.7396666401459 Newton --> No Conversion Required
FINAL ANSWER
10.7396666401459 10.73967 Newton <-- Sum of all Tangential Component
(Calculation completed in 00.004 seconds)

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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 Tangential Component given Factor of Safety Formula

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
ΣT = ((cu*L')+(ΣN*tan((φ*pi)/180)))/fs

What is Tangential Force?

Tangential force is defined as the force acting on a moving body in the direction of the tangent to the curved path of the body. If the velocity of the object is positive, the acceleration will be negative.

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

Sum of Tangential Component given Factor of Safety calculator uses 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 to calculate the Sum of all Tangential Component, The Sum of Tangential Component given Factor of Safety is defined as the ratio of allowable stress to actual stress; Sum of tangential component ensures stability and safety. Sum of all Tangential Component is denoted by ΣT symbol.

How to calculate Sum of Tangential Component given Factor of Safety using this online calculator? To use this online calculator for Sum of Tangential Component given Factor of Safety, enter Unit Cohesion (cu), Length of Slip Arc (L'), Sum of all Normal Component (ΣN), Angle of Internal Friction (φ) & Factor of Safety (fs) and hit the calculate button. Here is how the Sum of Tangential Component given Factor of Safety calculation can be explained with given input values -> 10.73931 = ((10*3.0001)+(5*tan((0.802851455917241*pi)/180)))/2.8.

FAQ

What is Sum of Tangential Component given Factor of Safety?
The Sum of Tangential Component given Factor of Safety is defined as the ratio of allowable stress to actual stress; Sum of tangential component ensures stability and safety and is represented as ΣT = ((cu*L')+(ΣN*tan((φ*pi)/180)))/fs or 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. 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 & Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
How to calculate Sum of Tangential Component given Factor of Safety?
The Sum of Tangential Component given Factor of Safety is defined as the ratio of allowable stress to actual stress; Sum of tangential component ensures stability and safety is calculated using 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. To calculate Sum of Tangential Component given Factor of Safety, you need Unit Cohesion (cu), Length of Slip Arc (L'), Sum of all Normal Component (ΣN), Angle of Internal Friction (φ) & Factor of Safety (fs). 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 & Factor of Safety 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 Sum of all Tangential Component?
In this formula, Sum of all Tangential Component uses Unit Cohesion, Length of Slip Arc, Sum of all Normal Component, Angle of Internal Friction & Factor of Safety. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Sum of all Tangential Component = Driving Moment/Radius of Slip Circle
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