Factor of Safety given Shear Force in Bishop's Analysis Calculator

✖Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.ⓘ Effective Cohesion [c']			+10% -10%
✖Length of Arc of the slice taken into consideration.ⓘ Length of Arc [l]			+10% -10%
✖Total normal force acting at the base of the slice.ⓘ Total Normal Force [P]			+10% -10%
✖Upward Force due to seepage water.ⓘ Upward Force [u]			+10% -10%
✖Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.ⓘ Effective Angle of Internal Friction [φ']			+10% -10%
✖Shear Force on Slice in Soil Mechanics acting along the base of slice.ⓘ Shear Force on Slice in Soil Mechanics [S]			+10% -10%

✖Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.ⓘ Factor of Safety given Shear Force in Bishop's Analysis [f_s]

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Formula

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Factor of Safety given Shear Force in Bishop's Analysis

Formula

f s = \frac{(c' \cdot l) + (P - (u \cdot l)) \cdot \tan (\frac{φ' \cdot π}{180})}{S}

Example

3.393238 = \frac{(4 Pa \cdot 9.42 m) + (150 N - (20 Pa \cdot 9.42 m)) \cdot \tan (\frac{9.99 ° \cdot π}{180})}{11.07 N}

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Factor of Safety given Shear Force in Bishop's Analysis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Factor of Safety = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics
f_s = ((c'*l)+(P-(u*l))*tan((φ'*pi)/180))/S
This formula uses 1 Constants, 1 Functions, 7 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

Factor of Safety - Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.
Effective Cohesion - (Measured in Pascal) - Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.
Length of Arc - (Measured in Meter) - Length of Arc of the slice taken into consideration.
Total Normal Force - (Measured in Newton) - Total normal force acting at the base of the slice.
Upward Force - (Measured in Pascal) - Upward Force due to seepage water.
Effective Angle of Internal Friction - (Measured in Radian) - Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.
Shear Force on Slice in Soil Mechanics - (Measured in Newton) - Shear Force on Slice in Soil Mechanics acting along the base of slice.

STEP 1: Convert Input(s) to Base Unit

Effective Cohesion: 4 Pascal --> 4 Pascal No Conversion Required
Length of Arc: 9.42 Meter --> 9.42 Meter No Conversion Required
Total Normal Force: 150 Newton --> 150 Newton No Conversion Required
Upward Force: 20 Pascal --> 20 Pascal No Conversion Required
Effective Angle of Internal Friction: 9.99 Degree --> 0.174358392274201 Radian (Check conversion here)
Shear Force on Slice in Soil Mechanics: 11.07 Newton --> 11.07 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_s = ((c'*l)+(P-(u*l))*tan((φ'*pi)/180))/S --> ((4*9.42)+(150-(20*9.42))*tan((0.174358392274201*pi)/180))/11.07

Evaluating ... ...

f_s = 3.39323789730528

STEP 3: Convert Result to Output's Unit

3.39323789730528 --> No Conversion Required

FINAL ANSWER

3.39323789730528 ≈ 3.393238 <-- Factor of Safety

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< Slope Stability Analysis using Bishops Method Calculators

Length of Arc of Slice given Effective Stress

Go Length of Arc = Total Normal Force/(Effective Normal Stress+Total Pore Pressure)

Effective Stress on Slice

Go Effective Normal Stress = (Total Normal Force/Length of Arc)-Total Pore Pressure

Normal Stress on Slice

Go Normal Stress in Pascal = Total Normal Force/Length of Arc

Length of Arc of Slice

Go Length of Arc = Total Normal Force/Normal Stress in Pascal

Factor of Safety given Shear Force in Bishop's Analysis Formula

What is Factor of Safety?

The ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design.

How to Calculate Factor of Safety given Shear Force in Bishop's Analysis?

Factor of Safety given Shear Force in Bishop's Analysis calculator uses Factor of Safety = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics to calculate the Factor of Safety, The Factor of Safety given Shear Force in Bishop's Analysis is defined as the value of factor of safety when we have prior information of other parameters used. Factor of Safety is denoted by f_s symbol.

How to calculate Factor of Safety given Shear Force in Bishop's Analysis using this online calculator? To use this online calculator for Factor of Safety given Shear Force in Bishop's Analysis, enter Effective Cohesion (c'), Length of Arc (l), Total Normal Force (P), Upward Force (u), Effective Angle of Internal Friction (φ') & Shear Force on Slice in Soil Mechanics (S) and hit the calculate button. Here is how the Factor of Safety given Shear Force in Bishop's Analysis calculation can be explained with given input values -> 7.408904 = ((4*9.42)+(150-(20*9.42))*tan((0.174358392274201*pi)/180))/11.07.

FAQ

What is Factor of Safety given Shear Force in Bishop's Analysis?

The Factor of Safety given Shear Force in Bishop's Analysis is defined as the value of factor of safety when we have prior information of other parameters used and is represented as f_s = ((c'*l)+(P-(u*l))*tan((φ'*pi)/180))/S or Factor of Safety = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics. Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation, Length of Arc of the slice taken into consideration, Total normal force acting at the base of the slice, Upward Force due to seepage water, Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction & Shear Force on Slice in Soil Mechanics acting along the base of slice.

How to calculate Factor of Safety given Shear Force in Bishop's Analysis?

The Factor of Safety given Shear Force in Bishop's Analysis is defined as the value of factor of safety when we have prior information of other parameters used is calculated using Factor of Safety = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics. To calculate Factor of Safety given Shear Force in Bishop's Analysis, you need Effective Cohesion (c'), Length of Arc (l), Total Normal Force (P), Upward Force (u), Effective Angle of Internal Friction (φ') & Shear Force on Slice in Soil Mechanics (S). With our tool, you need to enter the respective value for Effective Cohesion, Length of Arc, Total Normal Force, Upward Force, Effective Angle of Internal Friction & Shear Force on Slice in Soil Mechanics 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 Factor of Safety?

In this formula, Factor of Safety uses Effective Cohesion, Length of Arc, Total Normal Force, Upward Force, Effective Angle of Internal Friction & Shear Force on Slice in Soil Mechanics. We can use 1 other way(s) to calculate the same, which is/are as follows -

Factor of Safety = Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio)

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