Sum of Normal Component given Resisting Moment Solution

STEP 0: Pre-Calculation Summary
Formula Used
Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction))
ΣN = ((MR/r)-(cu*L'))/tan((φ))
This formula uses 1 Functions, 6 Variables
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 - (Measured in Newton) - Sum of all Normal Component means total normal force on slip circle.
Resisting Moment - (Measured in Kilonewton Meter) - Resisting Moment is a moment produced by internal tensile and compressive forces.
Radius of Slip Circle - (Measured in Meter) - Radius of Slip Circle is the distance between center and one point on slip circle.
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 - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .
STEP 1: Convert Input(s) to Base Unit
Resisting Moment: 20 Kilonewton Meter --> 20 Kilonewton Meter No Conversion Required
Radius of Slip Circle: 0.6 Meter --> 0.6 Meter 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: 46 Degree --> 0.802851455917241 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΣN = ((MR/r)-(cu*L'))/tan((φ)) --> ((20/0.6)-(10*3.0001))/tan((0.802851455917241))
Evaluating ... ...
ΣN = 3.21799689391641
STEP 3: Convert Result to Output's Unit
3.21799689391641 Newton --> No Conversion Required
FINAL ANSWER
3.21799689391641 3.217997 Newton <-- Sum of all Normal Component
(Calculation completed in 00.020 seconds)

Credits

Created by Suraj Kumar
Birsa Institute of Technology (BIT), Sindri
Suraj Kumar has created this Calculator and 2200+ more calculators!
Verified by Ishita Goyal
Meerut Institute of Engineering and Technology (MIET), Meerut
Ishita Goyal has verified this Calculator and 2600+ more calculators!

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 Resisting Moment Formula

Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction))
ΣN = ((MR/r)-(cu*L'))/tan((φ))

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.

How to Calculate Sum of Normal Component given Resisting Moment?

Sum of Normal Component given Resisting Moment calculator uses Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction)) to calculate the Sum of all Normal Component, The Sum of Normal Component given Resisting Moment is defined as the resisting moment caused by external loads in a static equilibrium condition. Sum of all Normal Component is denoted by ΣN symbol.

How to calculate Sum of Normal Component given Resisting Moment using this online calculator? To use this online calculator for Sum of Normal Component given Resisting Moment, enter Resisting Moment (MR), Radius of Slip Circle (r), Unit Cohesion (cu), Length of Slip Arc (L') & Angle of Internal Friction (φ) and hit the calculate button. Here is how the Sum of Normal Component given Resisting Moment calculation can be explained with given input values -> -19.319567 = ((20000/0.6)-(10*3.0001))/tan((0.802851455917241)).

FAQ

What is Sum of Normal Component given Resisting Moment?
The Sum of Normal Component given Resisting Moment is defined as the resisting moment caused by external loads in a static equilibrium condition and is represented as ΣN = ((MR/r)-(cu*L'))/tan((φ)) or Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction)). Resisting Moment is a moment produced by internal tensile and compressive forces, Radius of Slip Circle is the distance between center and one point on slip circle, 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 is the angle measured between the normal force and resultant force .
How to calculate Sum of Normal Component given Resisting Moment?
The Sum of Normal Component given Resisting Moment is defined as the resisting moment caused by external loads in a static equilibrium condition is calculated using Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction)). To calculate Sum of Normal Component given Resisting Moment, you need Resisting Moment (MR), Radius of Slip Circle (r), Unit Cohesion (cu), Length of Slip Arc (L') & Angle of Internal Friction (φ). With our tool, you need to enter the respective value for Resisting Moment, Radius of Slip Circle, Unit Cohesion, Length of Slip Arc & Angle of Internal Friction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!