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Total Normal Force Acting on Slice given Weight of Slice Formula

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

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

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

Total Normal Force Acting on Slice given Weight of Slice Example

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Here is how the Total Normal Force Acting on Slice given Weight of Slice equation looks like with Values.

Here is how the Total Normal Force Acting on Slice given Weight of Slice equation looks like with Units.

Here is how the Total Normal Force Acting on Slice given Weight of Slice equation looks like.

12.8695 = \frac{20 + 2.89 - 9.87 - (11.07 \cdot \sin (\frac{45 \cdot 3.1416}{180}))}{\cos (\frac{45 \cdot 3.1416}{180})}

12.8695N = \frac{20N + 2.89N - 9.87N - (11.07N \cdot \sin (\frac{45° \cdot 3.1416}{180}))}{\cos (\frac{45° \cdot 3.1416}{180})}

12.8695 = \frac{20 + 2.89 - 9.87 - (11.07 \cdot \sin (\frac{45 \cdot 3.1416}{180}))}{\cos (\frac{45 \cdot 3.1416}{180})}

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Total Normal Force Acting on Slice given Weight of Slice Solution

Follow our step by step solution on how to calculate Total Normal Force Acting on Slice given Weight of Slice?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

F n = \frac{20N + 2.89N - 9.87N - (11.07N \cdot \sin (\frac{45° \cdot π}{180}))}{\cos (\frac{45° \cdot π}{180})}

Next Step Substitute values of Constants

∴

F n = \frac{20N + 2.89N - 9.87N - (11.07N \cdot \sin (\frac{45° \cdot 3.1416}{180}))}{\cos (\frac{45° \cdot 3.1416}{180})}

Next Step Convert Units

∴

F n = \frac{20N + 2.89N - 9.87N - (11.07N \cdot \sin (\frac{0.7854rad \cdot 3.1416}{180}))}{\cos (\frac{0.7854rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

F n = \frac{20 + 2.89 - 9.87 - (11.07 \cdot \sin (\frac{0.7854 \cdot 3.1416}{180}))}{\cos (\frac{0.7854 \cdot 3.1416}{180})}

Next Step Evaluate

∴

F n = 12.8694686736617N

LAST Step Rounding Answer

∴

F n = 12.8695N

Total Normal Force Acting on Slice given Weight of Slice Formula Elements

Variables

Constants

Functions

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

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

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

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

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

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

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 Total Normal Force Acting on Slice given Weight of Slice?

Total Normal Force Acting on Slice given Weight of Slice evaluator 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 evaluate 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 evaluate Total Normal Force Acting on Slice given Weight of Slice using this online evaluator? To use this online evaluator 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.

FAQs on Total Normal Force Acting on Slice given Weight of Slice

What is the formula to find Total Normal Force Acting on Slice given Weight of Slice?

The formula of Total Normal Force Acting on Slice given Weight of Slice is expressed as 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). Here is an example- 12.86947 = (20+2.89-9.87-(11.07*sin((0.785398163397301*pi)/180)))/cos((0.785398163397301*pi)/180).

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

With 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) we can find Total Normal Force Acting on Slice given Weight of Slice using the formula - 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). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

Can the Total Normal Force Acting on Slice given Weight of Slice be negative?

No, the Total Normal Force Acting on Slice given Weight of Slice, measured in Force cannot be negative.

Which unit is used to measure Total Normal Force Acting on Slice given Weight of Slice?

Total Normal Force Acting on Slice given Weight of Slice is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Total Normal Force Acting on Slice given Weight of Slice can be measured.

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Total Normal Force Acting on Slice given Weight of Slice Formula

Total Normal Force Acting on Slice given Weight of Slice Example

Total Normal Force Acting on Slice given Weight of Slice Solution

Total Normal Force Acting on Slice given Weight of Slice Formula Elements

Other formulas in Slope Stability Analysis using Bishops Method category

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

FAQs on Total Normal Force Acting on Slice given Weight of Slice

Variable Name