Total Normal Force Acting on Slice given Weight of Slice Calculator

✖Weight of Slice taken in Bishop's method.ⓘ Weight of Slice [W]			+10% -10%
✖Vertical Shear Force on the section N.ⓘ Vertical Shear Force [X_n]			+10% -10%
✖Vertical Shear Force at other Section means shear force at section N+1.ⓘ Vertical Shear Force at other Section [X_(n+1)]			+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%
✖Angle of Base of the slice with horizontal.ⓘ Angle of Base [θ]			+10% -10%

✖Total Normal Force in Soil Mechanics is the force that surfaces exert to prevent solid objects from passing through each other.ⓘ Total Normal Force Acting on Slice given Weight of Slice [F_n]

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Formula

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Total Normal Force Acting on Slice given Weight of Slice

Formula

`"F"_{"n"} = ("W"+"X"_{"n"}-"X"_{"(n+1)"}-("S"*sin(("θ"*pi)/180)))/cos(("θ"*pi)/180)`

Example

`"12.86947N"=("20.0N"+"2.89N"-"9.87N"-("11.07N"*sin(("45°"*pi)/180)))/cos(("45°"*pi)/180)`

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Download Slope Stability Analysis using Bishops Method Formulas PDF

Total Normal Force Acting on Slice given Weight of Slice Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Normal Force in Soil Mechanics = (Weight of Slice+Vertical Shear Force-Vertical Shear Force at other Section-(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180)))/cos((Angle of Base*pi)/180)
F_n = (W+X_n-X_(n+1)-(S*sin((θ*pi)/180)))/cos((θ*pi)/180)
This formula uses 1 Constants, 2 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Total Normal Force in Soil Mechanics - (Measured in Newton) - Total Normal Force in Soil Mechanics is the force that surfaces exert to prevent solid objects from passing through each other.
Weight of Slice - (Measured in Newton) - Weight of Slice taken in Bishop's method.
Vertical Shear Force - (Measured in Newton) - Vertical Shear Force on the section N.
Vertical Shear Force at other Section - (Measured in Newton) - Vertical Shear Force at other Section means shear force at section N+1.
Shear Force on Slice in Soil Mechanics - (Measured in Newton) - Shear Force on Slice in Soil Mechanics acting along the base of slice.
Angle of Base - (Measured in Radian) - Angle of Base of the slice with horizontal.

STEP 1: Convert Input(s) to Base Unit

Weight of Slice: 20 Newton --> 20 Newton No Conversion Required
Vertical Shear Force: 2.89 Newton --> 2.89 Newton No Conversion Required
Vertical Shear Force at other Section: 9.87 Newton --> 9.87 Newton No Conversion Required
Shear Force on Slice in Soil Mechanics: 11.07 Newton --> 11.07 Newton No Conversion Required
Angle of Base: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_n = (W+X_n-X_(n+1)-(S*sin((θ*pi)/180)))/cos((θ*pi)/180) --> (20+2.89-9.87-(11.07*sin((0.785398163397301*pi)/180)))/cos((0.785398163397301*pi)/180)

Evaluating ... ...

F_n = 12.8694686736617

STEP 3: Convert Result to Output's Unit

12.8694686736617 Newton --> No Conversion Required

FINAL ANSWER

12.8694686736617 ≈ 12.86947 Newton <-- Total Normal Force 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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< 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

Total Normal Force Acting on Slice given Weight of Slice 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.

How to Calculate Total Normal Force Acting on Slice given Weight of Slice?

Total Normal Force Acting on Slice given Weight of Slice calculator uses Total Normal Force in Soil Mechanics = (Weight of Slice+Vertical Shear Force-Vertical Shear Force at other Section-(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180)))/cos((Angle of Base*pi)/180) to calculate the Total Normal Force in Soil Mechanics, The Total Normal Force Acting on Slice given Weight of Slice is defined as the value of total normal force when we have prior information of other parameters used. Total Normal Force in Soil Mechanics is denoted by F_n symbol.

How to calculate Total Normal Force Acting on Slice given Weight of Slice using this online calculator? To use this online calculator for Total Normal Force Acting on Slice given Weight of Slice, enter Weight of Slice (W), Vertical Shear Force (X_n), Vertical Shear Force at other Section (X_(n+1)), Shear Force on Slice in Soil Mechanics (S) & Angle of Base (θ) and hit the calculate button. Here is how the Total Normal Force Acting on Slice given Weight of Slice calculation can be explained with given input values -> 12.86947 = (20+2.89-9.87-(11.07*sin((0.785398163397301*pi)/180)))/cos((0.785398163397301*pi)/180).

FAQ

What is Total Normal Force Acting on Slice given Weight of Slice?

The Total Normal Force Acting on Slice given Weight of Slice is defined as the value of total normal force when we have prior information of other parameters used and is represented as F_n = (W+X_n-X_(n+1)-(S*sin((θ*pi)/180)))/cos((θ*pi)/180) or Total Normal Force in Soil Mechanics = (Weight of Slice+Vertical Shear Force-Vertical Shear Force at other Section-(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180)))/cos((Angle of Base*pi)/180). Weight of Slice taken in Bishop's method, Vertical Shear Force on the section N, Vertical Shear Force at other Section means shear force at section N+1, Shear Force on Slice in Soil Mechanics acting along the base of slice & Angle of Base of the slice with horizontal.

How to calculate Total Normal Force Acting on Slice given Weight of Slice?

The Total Normal Force Acting on Slice given Weight of Slice is defined as the value of total normal force when we have prior information of other parameters used is calculated using Total Normal Force in Soil Mechanics = (Weight of Slice+Vertical Shear Force-Vertical Shear Force at other Section-(Shear Force on Slice in Soil Mechanics*sin((Angle of Base*pi)/180)))/cos((Angle of Base*pi)/180). To calculate Total Normal Force Acting on Slice given Weight of Slice, you need Weight of Slice (W), Vertical Shear Force (X_n), Vertical Shear Force at other Section (X_(n+1)), Shear Force on Slice in Soil Mechanics (S) & Angle of Base (θ). With our tool, you need to enter the respective value for Weight of Slice, Vertical Shear Force, Vertical Shear Force at other Section, Shear Force on Slice in Soil Mechanics & Angle of Base 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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