Shear Strength given Normal Stress on Slice 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%
✖Normal Stress in Pascal is defined as the stress produced by the perpendicular action of a force on a given area.ⓘ Normal Stress in Pascal [σ_normal]			+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 Strength of Soil in Pascal is the strength of a material against the structural failure when the material fails in shear.ⓘ Shear Strength given Normal Stress on Slice [τ]

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Formula

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Shear Strength given Normal Stress on Slice

Formula

`"τ" = ("c'"+("σ"_{"normal"}-"u")*tan(("φ'"*pi)/180))`

Example

`"3.986945Pa"=("4Pa"+("15.71Pa"-"20Pa")*tan(("9.99°"*pi)/180))`

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Download Slope Stability Analysis using Bishops Method Formulas PDF

Shear Strength given Normal Stress on Slice Solution

STEP 0: Pre-Calculation Summary

Formula Used

Shear Strength of Soil in Pascal = (Effective Cohesion+(Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180))
τ = (c'+(σ_normal-u)*tan((φ'*pi)/180))
This formula uses 1 Constants, 1 Functions, 5 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

Shear Strength of Soil in Pascal - (Measured in Pascal) - Shear Strength of Soil in Pascal is the strength of a material against the structural failure when the material fails in shear.
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.
Normal Stress in Pascal - (Measured in Pascal) - Normal Stress in Pascal is defined as the stress produced by the perpendicular action of a force on a given area.
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.

STEP 1: Convert Input(s) to Base Unit

Effective Cohesion: 4 Pascal --> 4 Pascal No Conversion Required
Normal Stress in Pascal: 15.71 Pascal --> 15.71 Pascal 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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ = (c'+(σ_normal-u)*tan((φ'*pi)/180)) --> (4+(15.71-20)*tan((0.174358392274201*pi)/180))

Evaluating ... ...

τ = 3.98694494047909

STEP 3: Convert Result to Output's Unit

3.98694494047909 Pascal --> No Conversion Required

FINAL ANSWER

3.98694494047909 ≈ 3.986945 Pascal <-- Shear Strength of Soil in Pascal

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< 25 Slope Stability Analysis using Bishops Method Calculators

Weight of Slice given Total Normal Force Acting on Slice

Go Weight of Slice = (Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))-Vertical Shear Force+Vertical Shear Force at other Section

Resultant Vertical Shear Force on Section N+1

Go Vertical Shear Force at other Section = Weight of Slice+Vertical Shear Force-(Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))

Resultant Vertical Shear Force on Section N

Go Vertical Shear Force = (Total Normal Force in Soil Mechanics*cos((Angle of Base*pi)/180))+(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180))-Weight of Slice+Vertical Shear Force at other Section

Effective Cohesion of Soil given Shear Force in Bishop's Analysis

Go Effective Cohesion = ((Shear Force on Slice in Soil Mechanics*Factor of Safety)-((Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180)))/Length of Arc

Factor of Safety given Shear Force in Bishop's Analysis

Go 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 Angle of Internal Friction given Shear Force in Bishop's Analysis

Go Effective Angle of Internal Friction = atan(((Shear Force on Slice in Soil Mechanics*Factor of Safety)-(Effective Cohesion*Length of Arc))/(Total Normal Force-(Upward Force*Length of Arc)))

Effective Cohesion of Soil given Normal Stress on Slice

Go Effective Cohesion = Shear Strength of Soil in Pascal-((Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180))

Normal Stress on Slice given Shear Strength

Go Normal Stress in Pascal = ((Shear Strength of Soil in Pascal-Cohesion in Soil)/tan((Effective Angle of Internal Friction*pi)/180))+Upward Force

Effective Angle of Internal Friction given Shear Strength

Go Effective Angle of Internal Friction = atan((Shear Strength-Effective Cohesion)/(Normal Stress in Mega Pascal-Upward Force))

Radius of Arc when Total Shear Force on Slice is Available

Go Radius of Soil Section = (Total Weight of Slice in Soil Mechanics*Horizontal Distance)/Total Shear Force in Soil Mechanics

Total Weight of Slice given Total Shear Force on Slice

Go Total Weight of Slice in Soil Mechanics = (Total Shear Force in Soil Mechanics*Radius of Soil Section)/Horizontal Distance

Horizontal Distance of Slice from Centre of Rotation

Go Horizontal Distance = (Total Shear Force in Soil Mechanics*Radius of Soil Section)/Total Weight of Slice in Soil Mechanics

Factor of Safety given by Bishop

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

Pore Pressure Ratio given Horizontal Width

Go Pore Pressure Ratio = (Upward Force*Width of Soil Section)/Total Weight of Slice in Soil Mechanics

Unit weight of Soil given Pore Pressure Ratio

Go Unit Weight of Soil = (Upward Force in Seepage Analysis/(Pore Pressure Ratio*Height of Slice))

Height of Slice given Pore Pressure Ratio

Go Height of Slice = (Upward Force in Seepage Analysis/(Pore Pressure Ratio*Unit Weight of Soil))

Pore Pressure Ratio given Unit Weight

Go Pore Pressure Ratio = (Upward Force in Seepage Analysis/(Unit Weight of Soil*Height of Slice))

Length of Arc of Slice given Effective Stress

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

Pore Pressure given Effective Stress on Slice

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

Effective Stress on Slice

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

Length of Arc of Slice given Shear Force in Bishop's Analysis

Go Length of Arc = Shear Force on Slice in Soil Mechanics/Shear Stress of Soil in Pascal

Change in Pore Pressure given Overall Pore Pressure Coefficient

Go Change in Pore Pressure = Change in Normal Stress*Pore Pressure Coefficient Overall

Change in Normal Stress given Overall Pore Pressure Coefficient

Go Change in Normal Stress = Change in Pore Pressure/Pore Pressure Coefficient Overall

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

Shear Strength given Normal Stress on Slice Formula

Shear Strength of Soil in Pascal = (Effective Cohesion+(Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180))
τ = (c'+(σ_normal-u)*tan((φ'*pi)/180))

What is Shear Strength?

Shear strength is the strength of a material or component against the type of yield or structural failure when the material or component fails in shear. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force.

How to Calculate Shear Strength given Normal Stress on Slice?

Shear Strength given Normal Stress on Slice calculator uses Shear Strength of Soil in Pascal = (Effective Cohesion+(Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180)) to calculate the Shear Strength of Soil in Pascal, The Shear Strength given Normal Stress on Slice is defined as the force acting in direction that's parallel to surface or cross section of body influencing slope stability. Shear Strength of Soil in Pascal is denoted by τ symbol.

How to calculate Shear Strength given Normal Stress on Slice using this online calculator? To use this online calculator for Shear Strength given Normal Stress on Slice, enter Effective Cohesion (c'), Normal Stress in Pascal (σ_normal), Upward Force (u) & Effective Angle of Internal Friction (φ') and hit the calculate button. Here is how the Shear Strength given Normal Stress on Slice calculation can be explained with given input values -> 3.986945 = (4+(15.71-20)*tan((0.174358392274201*pi)/180)).

FAQ

What is Shear Strength given Normal Stress on Slice?

The Shear Strength given Normal Stress on Slice is defined as the force acting in direction that's parallel to surface or cross section of body influencing slope stability and is represented as τ = (c'+(σ_normal-u)*tan((φ'*pi)/180)) or Shear Strength of Soil in Pascal = (Effective Cohesion+(Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180)). 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, Normal Stress in Pascal is defined as the stress produced by the perpendicular action of a force on a given area, Upward Force due to seepage water & Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.

How to calculate Shear Strength given Normal Stress on Slice?

The Shear Strength given Normal Stress on Slice is defined as the force acting in direction that's parallel to surface or cross section of body influencing slope stability is calculated using Shear Strength of Soil in Pascal = (Effective Cohesion+(Normal Stress in Pascal-Upward Force)*tan((Effective Angle of Internal Friction*pi)/180)). To calculate Shear Strength given Normal Stress on Slice, you need Effective Cohesion (c'), Normal Stress in Pascal (σ_normal), Upward Force (u) & Effective Angle of Internal Friction (φ'). With our tool, you need to enter the respective value for Effective Cohesion, Normal Stress in Pascal, Upward Force & Effective 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.

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