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Shear Force in Bishop's Analysis given Factor of Safety Formula

GoShear Force in Bishop's Analysis Formula

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

S = \frac{(c' \cdot l) + (P - (u \cdot l)) \cdot \tan (\frac{φ' \cdot π}{180})}{f s}

S - Shear Force on Slice in Soil Mechanics?c' - Effective Cohesion?l - Length of Arc?P - Total Normal Force?u - Upward Force?φ' - Effective Angle of Internal Friction?f_s - Factor of Safety?π - Archimedes' constant?

Shear Force in Bishop's Analysis given Factor of Safety Example

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Here is how the Shear Force in Bishop's Analysis given Factor of Safety equation looks like with Values.

Here is how the Shear Force in Bishop's Analysis given Factor of Safety equation looks like with Units.

Here is how the Shear Force in Bishop's Analysis given Factor of Safety equation looks like.

13.4154 = \frac{(4 \cdot 9.42) + (150 - (20 \cdot 9.42)) \cdot \tan (\frac{9.99 \cdot 3.1416}{180})}{2.8}

13.4154N = \frac{(4Pa \cdot 9.42m) + (150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot 3.1416}{180})}{2.8}

13.4154 = \frac{(4 \cdot 9.42) + (150 - (20 \cdot 9.42)) \cdot \tan (\frac{9.99 \cdot 3.1416}{180})}{2.8}

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Shear Force in Bishop's Analysis given Factor of Safety Solution

Follow our step by step solution on how to calculate Shear Force in Bishop's Analysis given Factor of Safety?

FIRST Step Consider the formula

S = \frac{(c' \cdot l) + (P - (u \cdot l)) \cdot \tan (\frac{φ' \cdot π}{180})}{f s}

Next Step Substitute values of Variables

∴

S = \frac{(4Pa \cdot 9.42m) + (150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot π}{180})}{2.8}

Next Step Substitute values of Constants

∴

S = \frac{(4Pa \cdot 9.42m) + (150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot 3.1416}{180})}{2.8}

Next Step Convert Units

∴

S = \frac{(4Pa \cdot 9.42m) + (150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{0.1744rad \cdot 3.1416}{180})}{2.8}

Next Step Prepare to Evaluate

∴

S = \frac{(4 \cdot 9.42) + (150 - (20 \cdot 9.42)) \cdot \tan (\frac{0.1744 \cdot 3.1416}{180})}{2.8}

Next Step Evaluate

∴

S = 13.4154084011319N

LAST Step Rounding Answer

∴

S = 13.4154N

Shear Force in Bishop's Analysis given Factor of Safety Formula Elements

Variables

Constants

Functions

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

Effective Cohesion

Effective Cohesion is the consistency of soft to hard defined on the basis of the standard CSN 73 1001 for different states of consistency and degree of saturation.

Symbol: c'

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Effective Cohesion

Length of Arc

Length of Arc of the slice taken into consideration.

Symbol: l

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Arc

Total Normal Force

Total normal force acting at the base of the slice.

Symbol: P

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Total Normal Force

Upward Force

Upward Force due to seepage water.

Symbol: u

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Upward Force

Effective Angle of Internal Friction

Effective Angle of Internal Friction is a measure of the shear strength of soils due to friction.

Symbol: φ'

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Effective Angle of Internal Friction

Factor of Safety

Factor of Safety expresses how much stronger a system is than it needs to be for an intended load.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

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

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other Formulas to find Shear Force on Slice in Soil Mechanics

Go Shear Force in Bishop's Analysis

S = 𝜏 \cdot l

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}

How to Evaluate Shear Force in Bishop's Analysis given Factor of Safety?

Shear Force in Bishop's Analysis given Factor of Safety evaluator uses Shear Force on Slice in Soil Mechanics = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Factor of Safety to evaluate the Shear Force on Slice in Soil Mechanics, The Shear Force in Bishop's Analysis given Factor of Safety is defined as a force acting in a direction that's parallel to (over the top of) a surface or cross section of a body influencing slope stability. Shear Force on Slice in Soil Mechanics is denoted by S symbol.

How to evaluate Shear Force in Bishop's Analysis given Factor of Safety using this online evaluator? To use this online evaluator for Shear Force in Bishop's Analysis given Factor of Safety, enter Effective Cohesion (c'), Length of Arc (l), Total Normal Force (P), Upward Force (u), Effective Angle of Internal Friction (φ') & Factor of Safety (f_s) and hit the calculate button.

FAQs on Shear Force in Bishop's Analysis given Factor of Safety

What is the formula to find Shear Force in Bishop's Analysis given Factor of Safety?

The formula of Shear Force in Bishop's Analysis given Factor of Safety is expressed as Shear Force on Slice in Soil Mechanics = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Factor of Safety. Here is an example- 13.41541 = ((4*9.42)+(150-(20*9.42))*tan((0.174358392274201*pi)/180))/2.8.

How to calculate Shear Force in Bishop's Analysis given Factor of Safety?

With Effective Cohesion (c'), Length of Arc (l), Total Normal Force (P), Upward Force (u), Effective Angle of Internal Friction (φ') & Factor of Safety (f_s) we can find Shear Force in Bishop's Analysis given Factor of Safety using the formula - Shear Force on Slice in Soil Mechanics = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Factor of Safety. This formula also uses Archimedes' constant and Tangent function(s).

What are the other ways to Calculate Shear Force on Slice in Soil Mechanics?

Here are the different ways to Calculate Shear Force on Slice in Soil Mechanics-

Shear Force on Slice in Soil Mechanics=Shear Stress of Soil in Pascal*Length of Arc

Can the Shear Force in Bishop's Analysis given Factor of Safety be negative?

No, the Shear Force in Bishop's Analysis given Factor of Safety, measured in Force cannot be negative.

Which unit is used to measure Shear Force in Bishop's Analysis given Factor of Safety?

Shear Force in Bishop's Analysis given Factor of Safety is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Shear Force in Bishop's Analysis given Factor of Safety can be measured.

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Shear Force in Bishop's Analysis given Factor of Safety Formula

​GoShear Force in Bishop's Analysis Formula

Shear Force in Bishop's Analysis given Factor of Safety Example

Shear Force in Bishop's Analysis given Factor of Safety Solution

Shear Force in Bishop's Analysis given Factor of Safety Formula Elements

Other Formulas to find Shear Force on Slice in Soil Mechanics

Other formulas in Slope Stability Analysis using Bishops Method category

How to Evaluate Shear Force in Bishop's Analysis given Factor of Safety?

FAQs on Shear Force in Bishop's Analysis given Factor of Safety

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GoShear Force in Bishop's Analysis Formula