Resultant Vertical Shear Force on Section N+1 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%
✖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%

✖Vertical Shear Force at other Section means shear force at section N+1.ⓘ Resultant Vertical Shear Force on Section N+1 [X_(n+1)]

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Formula

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Resultant Vertical Shear Force on Section N+1

Formula

X (n+1) = W + X n - (F n \cdot \cos (\frac{θ \cdot π}{180})) + (S \cdot \sin (\frac{θ \cdot π}{180}))

Example

10.95288 N = 20.0 N + 2.89 N - (12.09 N \cdot \cos (\frac{45 ° \cdot π}{180})) + (11.07 N \cdot \sin (\frac{45 ° \cdot π}{180}))

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Resultant Vertical Shear Force on Section N+1 Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Vertical Shear Force at other Section - (Measured in Newton) - Vertical Shear Force at other Section means shear force at section N+1.
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.
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.

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
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

X_(n+1) = W+X_n-(F_n*cos((θ*pi)/180))+(S*sin((θ*pi)/180)) --> 20+2.89-(12.09*cos((0.785398163397301*pi)/180))+(11.07*sin((0.785398163397301*pi)/180))

Evaluating ... ...

X_(n+1) = 10.9528762733733

STEP 3: Convert Result to Output's Unit

10.9528762733733 Newton --> No Conversion Required

FINAL ANSWER

10.9528762733733 ≈ 10.95288 Newton <-- Vertical Shear Force at other Section

(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

Resultant Vertical Shear Force on Section N+1 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+1?

Resultant Vertical Shear Force on Section N+1 calculator uses 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)) to calculate the Vertical Shear Force at other Section, The Resultant Vertical Shear Force on Section N+1 is defined as the value of resultant vertical shear force when we have prior information of other parameters used. Vertical Shear Force at other Section is denoted by X_(n+1) symbol.

How to calculate Resultant Vertical Shear Force on Section N+1 using this online calculator? To use this online calculator for Resultant Vertical Shear Force on Section N+1, enter Weight of Slice (W), Vertical Shear Force (X_n), Total Normal Force in Soil Mechanics (F_n), Angle of Base (θ) & Shear Force on Slice in Soil Mechanics (S) and hit the calculate button. Here is how the Resultant Vertical Shear Force on Section N+1 calculation can be explained with given input values -> 10.95288 = 20+2.89-(12.09*cos((0.785398163397301*pi)/180))+(11.07*sin((0.785398163397301*pi)/180)).

FAQ

What is Resultant Vertical Shear Force on Section N+1?

The Resultant Vertical Shear Force on Section N+1 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+1) = W+X_n-(F_n*cos((θ*pi)/180))+(S*sin((θ*pi)/180)) or 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)). Weight of Slice taken in Bishop's method, Vertical Shear Force on the section N, 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.

How to calculate Resultant Vertical Shear Force on Section N+1?

The Resultant Vertical Shear Force on Section N+1 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 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)). To calculate Resultant Vertical Shear Force on Section N+1, you need Weight of Slice (W), Vertical Shear Force (X_n), Total Normal Force in Soil Mechanics (F_n), Angle of Base (θ) & Shear Force on Slice in Soil Mechanics (S). With our tool, you need to enter the respective value for Weight of Slice, Vertical Shear Force, Total Normal Force in Soil Mechanics, Angle of Base & 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.

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