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Resultant Vertical Shear Force on Section N Formula

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Vertical Shear Force on the section N. Check FAQs

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

X_n - Vertical Shear Force?F_n - Total Normal Force in Soil Mechanics?θ - Angle of Base?S - Shear Force on Slice in Soil Mechanics?W - Weight of Slice?X_(n+1) - Vertical Shear Force at other Section?π - Archimedes' constant?

Resultant Vertical Shear Force on Section N Example

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Here is how the Resultant Vertical Shear Force on Section N equation looks like with Values.

Here is how the Resultant Vertical Shear Force on Section N equation looks like with Units.

Here is how the Resultant Vertical Shear Force on Section N equation looks like.

2.1106 = (12.09 \cdot \cos (\frac{45 \cdot 3.1416}{180})) + (11.07 \cdot \sin (\frac{45 \cdot 3.1416}{180})) - 20 + 9.87

2.1106N = (12.09N \cdot \cos (\frac{45° \cdot 3.1416}{180})) + (11.07N \cdot \sin (\frac{45° \cdot 3.1416}{180})) - 20N + 9.87N

2.1106 = (12.09 \cdot \cos (\frac{45 \cdot 3.1416}{180})) + (11.07 \cdot \sin (\frac{45 \cdot 3.1416}{180})) - 20 + 9.87

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Resultant Vertical Shear Force on Section N Solution

Follow our step by step solution on how to calculate Resultant Vertical Shear Force on Section N?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

X n = (12.09N \cdot \cos (\frac{45° \cdot π}{180})) + (11.07N \cdot \sin (\frac{45° \cdot π}{180})) - 20N + 9.87N

Next Step Substitute values of Constants

∴

X n = (12.09N \cdot \cos (\frac{45° \cdot 3.1416}{180})) + (11.07N \cdot \sin (\frac{45° \cdot 3.1416}{180})) - 20N + 9.87N

Next Step Convert Units

∴

X n = (12.09N \cdot \cos (\frac{0.7854rad \cdot 3.1416}{180})) + (11.07N \cdot \sin (\frac{0.7854rad \cdot 3.1416}{180})) - 20N + 9.87N

Next Step Prepare to Evaluate

∴

X n = (12.09 \cdot \cos (\frac{0.7854 \cdot 3.1416}{180})) + (11.07 \cdot \sin (\frac{0.7854 \cdot 3.1416}{180})) - 20 + 9.87

Next Step Evaluate

∴

X n = 2.11060455757483N

LAST Step Rounding Answer

∴

X n = 2.1106N

Resultant Vertical Shear Force on Section N Formula Elements

Variables

Constants

Functions

Vertical Shear Force

Vertical Shear Force on the section N.

Symbol: X_n

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Vertical Shear Force

Total Normal Force in Soil Mechanics

Total Normal Force in Soil Mechanics is the force that surfaces exert to prevent solid objects from passing through each other.

Symbol: F_n

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Normal Force in Soil Mechanics

Angle of Base

Angle of Base of the slice with horizontal.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Base

Shear Force on Slice in Soil Mechanics

Shear Force on Slice in Soil Mechanics acting along the base of slice.

Symbol: S

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Shear Force on Slice in Soil Mechanics

Weight of Slice

Weight of Slice taken in Bishop's method.

Symbol: W

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Weight of Slice

Vertical Shear Force at other Section

Vertical Shear Force at other Section means shear force at section N+1.

Symbol: X_(n+1)

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Vertical Shear Force at other Section

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Slope Stability Analysis using Bishops Method category

Go Normal Stress on Slice

σ normal = \frac{P}{l}

Go Length of Arc of Slice

l = \frac{P}{σ normal}

Go Effective Stress on Slice

σ' = (\frac{P}{l}) - ΣU

Go Length of Arc of Slice given Effective Stress

l = \frac{P}{σ' + ΣU}

How to Evaluate Resultant Vertical Shear Force on Section N?

Resultant Vertical Shear Force on Section N evaluator 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 evaluate 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 evaluate Resultant Vertical Shear Force on Section N using this online evaluator? To use this online evaluator 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.

FAQs on Resultant Vertical Shear Force on Section N

What is the formula to find Resultant Vertical Shear Force on Section N?

The formula of Resultant Vertical Shear Force on Section N is expressed as 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. Here is an example- 2.110605 = (12.09*cos((0.785398163397301*pi)/180))+(11.07*sin((0.785398163397301*pi)/180))-20+9.87.

How to calculate Resultant Vertical Shear Force on Section N?

With 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)) we can find Resultant Vertical Shear Force on Section N using the formula - 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. This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

Can the Resultant Vertical Shear Force on Section N be negative?

No, the Resultant Vertical Shear Force on Section N, measured in Force cannot be negative.

Which unit is used to measure Resultant Vertical Shear Force on Section N?

Resultant Vertical Shear Force on Section N is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Resultant Vertical Shear Force on Section N can be measured.

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Resultant Vertical Shear Force on Section N Formula

Resultant Vertical Shear Force on Section N Example

Resultant Vertical Shear Force on Section N Solution

Resultant Vertical Shear Force on Section N Formula Elements

Other formulas in Slope Stability Analysis using Bishops Method category

How to Evaluate Resultant Vertical Shear Force on Section N?

FAQs on Resultant Vertical Shear Force on Section N

Variable Name