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

GoFactor of Safety given by Bishop Formula

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

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

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

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

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

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

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

3.3932 = \frac{(4 \cdot 9.42) + (150 - (20 \cdot 9.42)) \cdot \tan (\frac{9.99 \cdot 3.1416}{180})}{11.07}

3.3932 = \frac{(4Pa \cdot 9.42m) + (150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot 3.1416}{180})}{11.07N}

3.3932 = \frac{(4 \cdot 9.42) + (150 - (20 \cdot 9.42)) \cdot \tan (\frac{9.99 \cdot 3.1416}{180})}{11.07}

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

f s = \frac{(4Pa \cdot 9.42m) + (150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot π}{180})}{11.07N}

Next Step Substitute values of Constants

∴

f s = \frac{(4Pa \cdot 9.42m) + (150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{9.99° \cdot 3.1416}{180})}{11.07N}

Next Step Convert Units

∴

f s = \frac{(4Pa \cdot 9.42m) + (150N - (20Pa \cdot 9.42m)) \cdot \tan (\frac{0.1744rad \cdot 3.1416}{180})}{11.07N}

Next Step Prepare to Evaluate

∴

f s = \frac{(4 \cdot 9.42) + (150 - (20 \cdot 9.42)) \cdot \tan (\frac{0.1744 \cdot 3.1416}{180})}{11.07}

Next Step Evaluate

∴

f s = 3.39323789730528

LAST Step Rounding Answer

∴

f s = 3.3932

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

Variables

Constants

Functions

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

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

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

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 Factor of Safety

Go Factor of Safety given by Bishop

f s = m - (n \cdot r u)

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

Factor of Safety given Shear Force in Bishop's Analysis evaluator uses Factor of Safety = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics to evaluate the Factor of Safety, The Factor of Safety given Shear Force in Bishop's Analysis is defined as the value of factor of safety when we have prior information of other parameters used. Factor of Safety is denoted by f_s symbol.

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

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

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

The formula of Factor of Safety given Shear Force in Bishop's Analysis is expressed as Factor of Safety = ((Effective Cohesion*Length of Arc)+(Total Normal Force-(Upward Force*Length of Arc))*tan((Effective Angle of Internal Friction*pi)/180))/Shear Force on Slice in Soil Mechanics. Here is an example- 7.408904 = ((4*9.42)+(150-(20*9.42))*tan((0.174358392274201*pi)/180))/11.07.

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

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

What are the other ways to Calculate Factor of Safety?

Here are the different ways to Calculate Factor of Safety-

Factor of Safety=Stability Coefficient m in Soil Mechanics-(Stability Coefficient n*Pore Pressure Ratio)

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

​GoFactor of Safety given by Bishop Formula

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

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

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

Other Formulas to find Factor of Safety

Other formulas in Slope Stability Analysis using Bishops Method category

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

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

Variable Name

GoFactor of Safety given by Bishop Formula