Resultant Vertical Shear Force on Section N Calculator

✖Total Normal Force in Soil Mechanics is the force that surfaces exert to prevent solid objects from passing through each other.ⓘ Total Normal Force in Soil Mechanics [F_n]			+10% -10%
✖Angle of Base of the slice with horizontal.ⓘ Angle of Base [θ]			+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%
✖Weight of Slice taken in Bishop's method.ⓘ Weight of Slice [W]			+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%

✖Vertical Shear Force on the section N.ⓘ Resultant Vertical Shear Force on Section N [X_n]

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Formula

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Resultant Vertical Shear Force on Section N

Formula

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

Example

`"2.110605N"=("12.09N"*cos(("45°"*pi)/180))+("11.07N"*sin(("45°"*pi)/180))-"20.0N"+"9.87N"`

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Resultant Vertical Shear Force on Section N Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
X_n = (F_n*cos((θ*pi)/180))+(S*sin((θ*pi)/180))-W+X_(n+1)
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

Vertical Shear Force - (Measured in Newton) - Vertical Shear Force on the section N.
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.
Angle of Base - (Measured in Radian) - Angle of Base of the slice with horizontal.
Shear Force on Slice in Soil Mechanics - (Measured in Newton) - Shear Force on Slice in Soil Mechanics acting along the base of slice.
Weight of Slice - (Measured in Newton) - Weight of Slice taken in Bishop's method.
Vertical Shear Force at other Section - (Measured in Newton) - Vertical Shear Force at other Section means shear force at section N+1.

STEP 1: Convert Input(s) to Base Unit

Total Normal Force in Soil Mechanics: 12.09 Newton --> 12.09 Newton No Conversion Required
Angle of Base: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Shear Force on Slice in Soil Mechanics: 11.07 Newton --> 11.07 Newton No Conversion Required
Weight of Slice: 20 Newton --> 20 Newton No Conversion Required
Vertical Shear Force at other Section: 9.87 Newton --> 9.87 Newton No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

X_n = (F_n*cos((θ*pi)/180))+(S*sin((θ*pi)/180))-W+X_(n+1) --> (12.09*cos((0.785398163397301*pi)/180))+(11.07*sin((0.785398163397301*pi)/180))-20+9.87

Evaluating ... ...

X_n = 2.11060455757483

STEP 3: Convert Result to Output's Unit

2.11060455757483 Newton --> No Conversion Required

FINAL ANSWER

2.11060455757483 ≈ 2.110605 Newton <-- Vertical Shear Force

(Calculation completed in 00.020 seconds)

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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

Resultant Vertical Shear Force on Section N Formula

What is Shear Force?

A shear force is a force applied perpendicular to a surface, in opposition to an offset force acting in the opposite direction. This results in a shear strain. In simple terms, one part of the surface is pushed in one direction, while another part of the surface is pushed in the opposite direction.

How to Calculate Resultant Vertical Shear Force on Section N?

Resultant Vertical Shear Force on Section N calculator uses 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 to calculate the Vertical Shear Force, The Resultant Vertical Shear Force on Section N is defined as the value of resultant vertical shear force when we have prior information of other parameters used. Vertical Shear Force is denoted by X_n symbol.

How to calculate Resultant Vertical Shear Force on Section N using this online calculator? To use this online calculator for Resultant Vertical Shear Force on Section N, enter Total Normal Force in Soil Mechanics (F_n), Angle of Base (θ), Shear Force on Slice in Soil Mechanics (S), Weight of Slice (W) & Vertical Shear Force at other Section (X_(n+1)) and hit the calculate button. Here is how the Resultant Vertical Shear Force on Section N calculation can be explained with given input values -> 2.110605 = (12.09*cos((0.785398163397301*pi)/180))+(11.07*sin((0.785398163397301*pi)/180))-20+9.87.

FAQ

What is Resultant Vertical Shear Force on Section N?

The Resultant Vertical Shear Force on Section N is defined as the value of resultant vertical shear force when we have prior information of other parameters used and is represented as X_n = (F_n*cos((θ*pi)/180))+(S*sin((θ*pi)/180))-W+X_(n+1) or 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. Total Normal Force in Soil Mechanics is the force that surfaces exert to prevent solid objects from passing through each other, Angle of Base of the slice with horizontal, Shear Force on Slice in Soil Mechanics acting along the base of slice, Weight of Slice taken in Bishop's method & Vertical Shear Force at other Section means shear force at section N+1.

How to calculate Resultant Vertical Shear Force on Section N?

The Resultant Vertical Shear Force on Section N is defined as the value of resultant vertical shear force when we have prior information of other parameters used is calculated using 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. To calculate Resultant Vertical Shear Force on Section N, you need Total Normal Force in Soil Mechanics (F_n), Angle of Base (θ), Shear Force on Slice in Soil Mechanics (S), Weight of Slice (W) & Vertical Shear Force at other Section (X_(n+1)). With our tool, you need to enter the respective value for Total Normal Force in Soil Mechanics, Angle of Base, Shear Force on Slice in Soil Mechanics, Weight of Slice & Vertical Shear Force at other Section 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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