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Weight of Slice given Total Normal Force Acting on Slice Formula

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Weight of Slice taken in Bishop's method. Check FAQs

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

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

Weight of Slice given Total Normal Force Acting on Slice Example

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

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

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

19.2206 = (12.09 \cdot \cos (\frac{45 \cdot 3.1416}{180})) + (11.07 \cdot \sin (\frac{45 \cdot 3.1416}{180})) - 2.89 + 9.87

19.2206N = (12.09N \cdot \cos (\frac{45° \cdot 3.1416}{180})) + (11.07N \cdot \sin (\frac{45° \cdot 3.1416}{180})) - 2.89N + 9.87N

19.2206 = (12.09 \cdot \cos (\frac{45 \cdot 3.1416}{180})) + (11.07 \cdot \sin (\frac{45 \cdot 3.1416}{180})) - 2.89 + 9.87

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Weight of Slice given Total Normal Force Acting on Slice Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

W = (12.09N \cdot \cos (\frac{45° \cdot π}{180})) + (11.07N \cdot \sin (\frac{45° \cdot π}{180})) - 2.89N + 9.87N

Next Step Substitute values of Constants

∴

W = (12.09N \cdot \cos (\frac{45° \cdot 3.1416}{180})) + (11.07N \cdot \sin (\frac{45° \cdot 3.1416}{180})) - 2.89N + 9.87N

Next Step Convert Units

∴

W = (12.09N \cdot \cos (\frac{0.7854rad \cdot 3.1416}{180})) + (11.07N \cdot \sin (\frac{0.7854rad \cdot 3.1416}{180})) - 2.89N + 9.87N

Next Step Prepare to Evaluate

∴

W = (12.09 \cdot \cos (\frac{0.7854 \cdot 3.1416}{180})) + (11.07 \cdot \sin (\frac{0.7854 \cdot 3.1416}{180})) - 2.89 + 9.87

Next Step Evaluate

∴

W = 19.2206045575748N

LAST Step Rounding Answer

∴

W = 19.2206N

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

Variables

Constants

Functions

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

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

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

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 Weight of Slice given Total Normal Force Acting on Slice?

Weight of Slice given Total Normal Force Acting on Slice evaluator uses 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 to evaluate the Weight of Slice, The Weight of Slice given Total Normal Force Acting on Slice is defined as the value of weight of slice when we have prior information of other parameters used. Weight of Slice is denoted by W symbol.

How to evaluate Weight of Slice given Total Normal Force Acting on Slice using this online evaluator? To use this online evaluator for Weight of Slice given Total Normal Force Acting on Slice, enter Total Normal Force in Soil Mechanics (F_n), Angle of Base (θ), Shear Force on Slice in Soil Mechanics (S), Vertical Shear Force (X_n) & Vertical Shear Force at other Section (X_(n+1)) and hit the calculate button.

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

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

The formula of Weight of Slice given Total Normal Force Acting on Slice is expressed as 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. Here is an example- 19.2206 = (12.09*cos((0.785398163397301*pi)/180))+(11.07*sin((0.785398163397301*pi)/180))-2.89+9.87.

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

With Total Normal Force in Soil Mechanics (F_n), Angle of Base (θ), Shear Force on Slice in Soil Mechanics (S), Vertical Shear Force (X_n) & Vertical Shear Force at other Section (X_(n+1)) we can find Weight of Slice given Total Normal Force Acting on Slice using the formula - 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. This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

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

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

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

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

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Weight of Slice given Total Normal Force Acting on Slice Formula

Weight of Slice given Total Normal Force Acting on Slice Example

Weight of Slice given Total Normal Force Acting on Slice Solution

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

Other formulas in Slope Stability Analysis using Bishops Method category

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

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

Variable Name