Angle of Internal Friction 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%
✖Sum of all Normal Component means total normal force on slip circle.ⓘ Sum of all Normal Component [ΣN]			+10% -10%

✖Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction.ⓘ Angle of Internal Friction given Resisting Moment [Φ_i]

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Angle of Internal Friction given Resisting Moment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component)
Φ_i = atan(((M_R/r)-(c_u*L^'))/ΣN)
This formula uses 2 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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

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.
Resisting Moment - (Measured in Newton 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.
Sum of all Normal Component - (Measured in Newton) - Sum of all Normal Component means total normal force on slip circle.

STEP 1: Convert Input(s) to Base Unit

Resisting Moment: 45.05 Kilonewton Meter --> 45050 Newton Meter (Check conversion here)
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
Sum of all Normal Component: 5.01 Newton --> 5.01 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Φ_i = atan(((M_R/r)-(c_u*L^'))/ΣN) --> atan(((45050/0.6)-(10*3.0001))/5.01)

Evaluating ... ...

Φ_i = 1.57072957426257

STEP 3: Convert Result to Output's Unit

1.57072957426257 Radian -->89.996175361643 Degree (Check conversion here)

FINAL ANSWER

89.996175361643 ≈ 89.99618 Degree <-- Angle of Internal Friction of Soil

(Calculation completed in 00.004 seconds)

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< The Swedish Slip Circle Method Calculators

Radial Distance from Center of Rotation given Length of Slip Arc

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

Arc Angle given Length of Slip Arc

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

Moment of Resistance given Factor of Safety

LaTeX Go Moment of Resistance with Factor of Safety = Factor of Safety*Driving Moment

Driving Moment given Factor of Safety

LaTeX Go Driving Moment = Resisting Moment/Factor of Safety

Angle of Internal Friction given Resisting Moment Formula

LaTeX Go

Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component)
Φ_i = atan(((M_R/r)-(c_u*L^'))/ΣN)

What is Angle of Internal Friction?

The angle of internal friction is a physical property of earth materials or the slope of a linear representation of the shear strength of earth materials.

How to Calculate Angle of Internal Friction given Resisting Moment?

Angle of Internal Friction given Resisting Moment calculator uses Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component) to calculate the Angle of Internal Friction of Soil, The Angle of Internal Friction given Resisting Moment formula is defined as the angle at which a material's resisting moment equals the applied moment, stabilizing movement. Angle of Internal Friction of Soil is denoted by Φ_i symbol.

How to calculate Angle of Internal Friction given Resisting Moment using this online calculator? To use this online calculator for Angle of Internal Friction given Resisting Moment, enter Resisting Moment (M_R), Radius of Slip Circle (r), Unit Cohesion (c_u), Length of Slip Arc (L^') & Sum of all Normal Component (ΣN) and hit the calculate button. Here is how the Angle of Internal Friction given Resisting Moment calculation can be explained with given input values -> 5156.126 = atan(((45050/0.6)-(10*3.0001))/5.01).

FAQ

What is Angle of Internal Friction given Resisting Moment?

The Angle of Internal Friction given Resisting Moment formula is defined as the angle at which a material's resisting moment equals the applied moment, stabilizing movement and is represented as Φ_i = atan(((M_R/r)-(c_u*L^'))/ΣN) or Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component). 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 & Sum of all Normal Component means total normal force on slip circle.

How to calculate Angle of Internal Friction given Resisting Moment?

The Angle of Internal Friction given Resisting Moment formula is defined as the angle at which a material's resisting moment equals the applied moment, stabilizing movement is calculated using Angle of Internal Friction of Soil = atan(((Resisting Moment/Radius of Slip Circle)-(Unit Cohesion*Length of Slip Arc))/Sum of all Normal Component). To calculate Angle of Internal Friction given Resisting Moment, you need Resisting Moment (M_R), Radius of Slip Circle (r), Unit Cohesion (c_u), Length of Slip Arc (L^') & Sum of all Normal Component (ΣN). With our tool, you need to enter the respective value for Resisting Moment, Radius of Slip Circle, Unit Cohesion, Length of Slip Arc & Sum of all Normal Component 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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