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Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Formula

GoEffective Angle of Internal Friction given Shear Strength Formula

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

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

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

Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Example

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Here is how the Effective Angle of Internal Friction given Shear Force in Bishop's Analysis equation looks like with Values.

Here is how the Effective Angle of Internal Friction given Shear Force in Bishop's Analysis equation looks like with Units.

Here is how the Effective Angle of Internal Friction given Shear Force in Bishop's Analysis equation looks like.

9.8741 = a \tan (\frac{(11.07 \cdot 2.8) - (4 \cdot 9.42)}{150 - (20 \cdot 9.42)})

9.8741° = a \tan (\frac{(11.07N \cdot 2.8) - (4Pa \cdot 9.42m)}{150N - (20Pa \cdot 9.42m)})

9.8741 = a \tan (\frac{(11.07 \cdot 2.8) - (4 \cdot 9.42)}{150 - (20 \cdot 9.42)})

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Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Solution

Follow our step by step solution on how to calculate Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

φ' = a \tan (\frac{(11.07N \cdot 2.8) - (4Pa \cdot 9.42m)}{150N - (20Pa \cdot 9.42m)})

Next Step Prepare to Evaluate

∴

φ' = a \tan (\frac{(11.07 \cdot 2.8) - (4 \cdot 9.42)}{150 - (20 \cdot 9.42)})

Next Step Evaluate

∴

φ' = 0.17233587966936rad

Next Step Convert to Output's Unit

∴

φ' = 9.87411856373062°

LAST Step Rounding Answer

∴

φ' = 9.8741°

Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Formula Elements

Variables

Functions

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

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

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)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

Other Formulas to find Effective Angle of Internal Friction

Go Effective Angle of Internal Friction given Shear Strength

φ' = a \tan (\frac{ζ soil - c'}{σ nm - 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 Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

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

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

FAQs on Effective Angle of Internal Friction given Shear Force in Bishop's Analysis

What is the formula to find Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

The formula of Effective Angle of Internal Friction given Shear Force in Bishop's Analysis is expressed as Effective Angle of Internal Friction = atan(((Shear Force on Slice in Soil Mechanics*Factor of Safety)-(Effective Cohesion*Length of Arc))/(Total Normal Force-(Upward Force*Length of Arc))). Here is an example- 1801.86 = atan(((11.07*2.8)-(4*9.42))/(150-(20*9.42))).

How to calculate Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

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

What are the other ways to Calculate Effective Angle of Internal Friction?

Here are the different ways to Calculate Effective Angle of Internal Friction-

Effective Angle of Internal Friction=atan((Shear Strength-Effective Cohesion)/(Normal Stress in Mega Pascal-Upward Force))

Can the Effective Angle of Internal Friction given Shear Force in Bishop's Analysis be negative?

No, the Effective Angle of Internal Friction given Shear Force in Bishop's Analysis, measured in Angle cannot be negative.

Which unit is used to measure Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

Effective Angle of Internal Friction given Shear Force in Bishop's Analysis is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Effective Angle of Internal Friction given Shear Force in Bishop's Analysis can be measured.

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Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Formula

​GoEffective Angle of Internal Friction given Shear Strength Formula

Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Example

Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Solution

Effective Angle of Internal Friction given Shear Force in Bishop's Analysis Formula Elements

Other Formulas to find Effective Angle of Internal Friction

Other formulas in Slope Stability Analysis using Bishops Method category

How to Evaluate Effective Angle of Internal Friction given Shear Force in Bishop's Analysis?

FAQs on Effective Angle of Internal Friction given Shear Force in Bishop's Analysis

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GoEffective Angle of Internal Friction given Shear Strength Formula