Sum of Normal Component given Resisting Moment Calculator

✖Resisting Moment is the moment (or torque) that counteracts the applied moment or load that tends to cause rotation or failure in a soil mass or structure.ⓘ Resisting Moment [M_R]			+10% -10%
✖Radius of Slip Circle is the distance between center and one point on slip circle.ⓘ Radius of Slip Circle [r]			+10% -10%
✖Unit Cohesion is the shear strength property of a soil that is solely attributed to cohesive forces between soil particles.ⓘ 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 measure of the shear strength of soil due to friction.ⓘ Angle of Internal Friction of Soil [Φ_i]			+10% -10%

✖Sum of all Normal Component means total normal force on slip circle.ⓘ Sum of Normal Component given Resisting Moment [ΣN]

⎘ Copy

👎

Formula

✖

Sum of Normal Component given Resisting Moment

Formula

ΣN = \frac{(\frac{M R}{r}) - (c u \cdot L')}{\tan ((Φ i))}

Example

5.639274 N = \frac{(\frac{45.05 kN*m}{0.6 m}) - (10 Pa \cdot 3.0001 m)}{\tan ((82.87 °))}

Calculator

LaTeX

Reset

👍

Download The Swedish Slip Circle Method Formulas PDF PDF Image

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 of Soil))
ΣN = ((M_R/r)-(c_u*L^'))/tan((Φ_i))
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 the moment (or torque) that counteracts the applied moment or load that tends to cause rotation or failure in a soil mass or structure.
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 shear strength property of a soil that is solely attributed to cohesive forces between soil particles.
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 measure of the shear strength of soil due to friction.

STEP 1: Convert Input(s) to Base Unit

Resisting Moment: 45.05 Kilonewton Meter --> 45.05 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 of Soil: 82.87 Degree --> 1.44635435112743 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΣN = ((M_R/r)-(c_u*L^'))/tan((Φ_i)) --> ((45.05/0.6)-(10*3.0001))/tan((1.44635435112743))

Evaluating ... ...

ΣN = 5.63927429235379

STEP 3: Convert Result to Output's Unit

5.63927429235379 Newton --> No Conversion Required

FINAL ANSWER

5.63927429235379 ≈ 5.639274 Newton <-- Sum of all Normal Component

(Calculation completed in 00.004 seconds)

You are here -

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

Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2100+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< The Swedish Slip Circle Method Calculators

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)

Moment of Resistance given Factor of Safety

Go Moment of Resistance with Factor of Safety = 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 of Soil))
ΣN = ((M_R/r)-(c_u*L^'))/tan((Φ_i))

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 of Soil)) to calculate the Sum of all Normal Component, The Sum of Normal Component given Resisting Moment is defined as the sum of forces acting perpendicular (normal) to the potential failure plane in the soil or rock mass, considering resisting moment. 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 (M_R), Radius of Slip Circle (r), 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 Resisting Moment calculation can be explained with given input values -> 5.639274 = ((45050/0.6)-(10*3.0001))/tan((1.44635435112743)).

FAQ

What is Sum of Normal Component given Resisting Moment?

The Sum of Normal Component given Resisting Moment is defined as the sum of forces acting perpendicular (normal) to the potential failure plane in the soil or rock mass, considering resisting moment and is represented as ΣN = ((M_R/r)-(c_u*L^'))/tan((Φ_i)) or Sum of all Normal Component = ((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/tan((Angle of Internal Friction of Soil)). Resisting Moment is the moment (or torque) that counteracts the applied moment or load that tends to cause rotation or failure in a soil mass or structure, Radius of Slip Circle is the distance between center and one point on slip circle, Unit Cohesion is the shear strength property of a soil that is solely attributed to cohesive forces between soil particles, Length of Slip Arc is the length of the arc formed by slip circle & Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction.

How to calculate Sum of Normal Component given Resisting Moment?

The Sum of Normal Component given Resisting Moment is defined as the sum of forces acting perpendicular (normal) to the potential failure plane in the soil or rock mass, considering resisting moment 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 of Soil)). To calculate Sum of Normal Component given Resisting Moment, you need Resisting Moment (M_R), Radius of Slip Circle (r), 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 Resisting Moment, Radius of Slip Circle, 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.

Home

FREE PDFs

🔍 Search