Sum of Normal Component given Factor of Safety Calculator

✖Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.ⓘ Factor of Safety [f_s]			+10% -10%
✖Sum of All Tangential Component in Soil Mechanics means total tangential component.ⓘ Sum of All Tangential Component in Soil Mechanics [F_t]			+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 in Soil Mechanics is the total normal stress acting on a soil mass due to various factors such as self-weight, external loads, and pore water pressure.ⓘ Sum of Normal Component given Factor of Safety [ΣF_N]

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Formula

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Sum of Normal Component given Factor of Safety

Formula

ΣF N = \frac{(f s \cdot F t) - (c u \cdot L')}{\tan (\frac{Φ i \cdot π}{180})}

Example

31.64481 N = \frac{(2.8 \cdot 11.0 N) - (10 Pa \cdot 3.0001 m)}{\tan (\frac{82.87 ° \cdot π}{180})}

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Sum of Normal Component given Factor of Safety Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
ΣF_N = ((f_s*F_t)-(c_u*L^'))/tan((Φ_i*pi)/180)
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 Normal Component in Soil Mechanics - (Measured in Newton) - Sum of All Normal Component in Soil Mechanics is the total normal stress acting on a soil mass due to various factors such as self-weight, external loads, and pore water pressure.
Factor of Safety - Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.
Sum of All Tangential Component in Soil Mechanics - (Measured in Newton) - Sum of All Tangential Component in Soil Mechanics means total tangential component.
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

Factor of Safety: 2.8 --> No Conversion Required
Sum of All Tangential Component in Soil Mechanics: 11 Newton --> 11 Newton 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

ΣF_N = ((f_s*F_t)-(c_u*L^'))/tan((Φ_i*pi)/180) --> ((2.8*11)-(10*3.0001))/tan((1.44635435112743*pi)/180)

Evaluating ... ...

ΣF_N = 31.6448062796375

STEP 3: Convert Result to Output's Unit

31.6448062796375 Newton --> No Conversion Required

FINAL ANSWER

31.6448062796375 ≈ 31.64481 Newton <-- Sum of All Normal Component in Soil Mechanics

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< 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 Factor of Safety Formula

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. A normal stress will occur when a member is placed in tension or compression.

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

Sum of Normal Component given Factor of Safety calculator uses 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) to calculate the Sum of All Normal Component in Soil Mechanics, The Sum of Normal Component given Factor of Safety formula is defined as the sum of forces acting perpendicular (normal) to the potential failure plane in the soil or rock mass. This component is crucial in determining the stability of slopes or retaining structures. Sum of All Normal Component in Soil Mechanics is denoted by ΣF_N symbol.

How to calculate Sum of Normal Component given Factor of Safety using this online calculator? To use this online calculator for Sum of Normal Component given Factor of Safety, enter Factor of Safety (f_s), Sum of All Tangential Component in Soil Mechanics (F_t), 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 Factor of Safety calculation can be explained with given input values -> 483.1873 = ((2.8*11)-(10*3.0001))/tan((1.44635435112743*pi)/180).

FAQ

What is Sum of Normal Component given Factor of Safety?

The Sum of Normal Component given Factor of Safety formula is defined as the sum of forces acting perpendicular (normal) to the potential failure plane in the soil or rock mass. This component is crucial in determining the stability of slopes or retaining structures and is represented as ΣF_N = ((f_s*F_t)-(c_u*L^'))/tan((Φ_i*pi)/180) or 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). Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it, Sum of All Tangential Component in Soil Mechanics means total tangential component, 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 Factor of Safety?

The Sum of Normal Component given Factor of Safety formula is defined as the sum of forces acting perpendicular (normal) to the potential failure plane in the soil or rock mass. This component is crucial in determining the stability of slopes or retaining structures is calculated using 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). To calculate Sum of Normal Component given Factor of Safety, you need Factor of Safety (f_s), Sum of All Tangential Component in Soil Mechanics (F_t), 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 Factor of Safety, Sum of All Tangential Component in Soil Mechanics, 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.

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