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Weighted Friction Angle given Factor of Safety with respect to Shear Strength Formula

GoWeighted Friction Angle given Mobilised Friction Angle Formula

GoWeighted Friction Angle given Submerged Unit Weight Formula

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Weighted Friction Angle is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis. Check FAQs

φ w = a \tan ((\frac{γ'}{γ sat}) \cdot (\frac{\tan ((Φ i))}{f s}))

φ_w - Weighted Friction Angle?γ^' - Submerged Unit Weight?γ_sat - Saturated Unit Weight?Φ_i - Angle of Internal Friction of Soil?f_s - Factor of Safety?

Weighted Friction Angle given Factor of Safety with respect to Shear Strength Example

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Here is how the Weighted Friction Angle given Factor of Safety with respect to Shear Strength equation looks like with Values.

Here is how the Weighted Friction Angle given Factor of Safety with respect to Shear Strength equation looks like with Units.

Here is how the Weighted Friction Angle given Factor of Safety with respect to Shear Strength equation looks like.

83.5667 = a \tan ((\frac{31}{9.98}) \cdot (\frac{\tan ((82.87))}{2.8}))

83.5667° = a \tan ((\frac{31N/m³}{9.98N/m³}) \cdot (\frac{\tan ((82.87°))}{2.8}))

83.5667 = a \tan ((\frac{31}{9.98}) \cdot (\frac{\tan ((82.87))}{2.8}))

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Weighted Friction Angle given Factor of Safety with respect to Shear Strength Solution

Follow our step by step solution on how to calculate Weighted Friction Angle given Factor of Safety with respect to Shear Strength?

FIRST Step Consider the formula

φ w = a \tan ((\frac{γ'}{γ sat}) \cdot (\frac{\tan ((Φ i))}{f s}))

Next Step Substitute values of Variables

∴

φ w = a \tan ((\frac{31N/m³}{9.98N/m³}) \cdot (\frac{\tan ((82.87°))}{2.8}))

Next Step Convert Units

∴

φ w = a \tan ((\frac{31N/m³}{9.98N/m³}) \cdot (\frac{\tan ((1.4464rad))}{2.8}))

Next Step Prepare to Evaluate

∴

φ w = a \tan ((\frac{31}{9.98}) \cdot (\frac{\tan ((1.4464))}{2.8}))

Next Step Evaluate

∴

φ w = 1.45851353248699rad

Next Step Convert to Output's Unit

∴

φ w = 83.566669774237°

LAST Step Rounding Answer

∴

φ w = 83.5667°

Weighted Friction Angle given Factor of Safety with respect to Shear Strength Formula Elements

Variables

Functions

Weighted Friction Angle

Weighted Friction Angle is an effective measure combining materials' friction properties and their relative contributions in geotechnical engineering for stability analysis.

Symbol: φ_w

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Weighted Friction Angle

Submerged Unit Weight

Submerged Unit Weight is the effective weight of the soil per unit volume when it is submerged in water.

Symbol: γ^'

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight

Saturated Unit Weight

Saturated Unit Weight is the value of the unit weight of the soil when the soil is completely saturated with water that is all the soil pores are completely filled with water.

Symbol: γ_sat

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Saturated Unit Weight

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is a measure of the shear strength of soil due to friction.

Symbol: Φ_i

Measurement: AngleUnit: °

Note: Value should be between -180 to 180.

Formulas to find Angle of Internal Friction of Soil

Factor of Safety

Factor of Safety is a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it.

Symbol: f_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Factor of Safety

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 Weighted Friction Angle

Go Weighted Friction Angle given Mobilised Friction Angle

φ w = \frac{γ' \cdot φ m}{γ sat}

Go Weighted Friction Angle given Submerged Unit Weight

φ w = \frac{γ' \cdot φ iw}{γ sat}

Other formulas in Taylor's Stability Number and Stability Curves category

Go Submerged Unit Weight given Factor of Safety with respect to Shear Strength

γ' = \frac{\tan (\frac{φ w \cdot π}{180})}{(\frac{1}{γ sat}) \cdot (\frac{\tan (\frac{Φ i \cdot π}{180})}{f s})}

Go Factor of Safety with respect to Shear Strength

f s = ((\frac{γ'}{γ sat}) \cdot (\frac{\tan ((φ))}{\tan ((φ IF))}))

Go Saturated Unit Weight given Factor of Safety with respect to Shear Strength

γ sat = ((\frac{γ'}{\tan ((φ IF))}) \cdot (\frac{\tan ((φ))}{f s}))

Go Angle of Internal Friction given Factor of Safety

φ = a \tan (\frac{f s \cdot γ sat \cdot \tan ((φ IF))}{γ'})

How to Evaluate Weighted Friction Angle given Factor of Safety with respect to Shear Strength?

Weighted Friction Angle given Factor of Safety with respect to Shear Strength evaluator uses Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety)) to evaluate the Weighted Friction Angle, The Weighted Friction Angle given Factor of Safety with respect to Shear Strength is defined as angle of internal friction adjusted for Factor of Safety, ensuring stability in structures against shear strength failure. Weighted Friction Angle is denoted by φ_w symbol.

How to evaluate Weighted Friction Angle given Factor of Safety with respect to Shear Strength using this online evaluator? To use this online evaluator for Weighted Friction Angle given Factor of Safety with respect to Shear Strength, enter Submerged Unit Weight (γ^'), Saturated Unit Weight (γ_sat), Angle of Internal Friction of Soil (Φ_i) & Factor of Safety (f_s) and hit the calculate button.

FAQs on Weighted Friction Angle given Factor of Safety with respect to Shear Strength

What is the formula to find Weighted Friction Angle given Factor of Safety with respect to Shear Strength?

The formula of Weighted Friction Angle given Factor of Safety with respect to Shear Strength is expressed as Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety)). Here is an example- 4788.017 = atan((31/9.98)*(tan((1.44635435112743))/2.8)).

How to calculate Weighted Friction Angle given Factor of Safety with respect to Shear Strength?

With Submerged Unit Weight (γ^'), Saturated Unit Weight (γ_sat), Angle of Internal Friction of Soil (Φ_i) & Factor of Safety (f_s) we can find Weighted Friction Angle given Factor of Safety with respect to Shear Strength using the formula - Weighted Friction Angle = atan((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction of Soil))/Factor of Safety)). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

What are the other ways to Calculate Weighted Friction Angle?

Here are the different ways to Calculate Weighted Friction Angle-

Weighted Friction Angle=(Submerged Unit Weight*Angle of Mobilized Friction)/Saturated Unit Weight
Weighted Friction Angle=(Submerged Unit Weight*Internal Friction Angle with Weighted Frict. Angle)/Saturated Unit Weight

Can the Weighted Friction Angle given Factor of Safety with respect to Shear Strength be negative?

No, the Weighted Friction Angle given Factor of Safety with respect to Shear Strength, measured in Angle cannot be negative.

Which unit is used to measure Weighted Friction Angle given Factor of Safety with respect to Shear Strength?

Weighted Friction Angle given Factor of Safety with respect to Shear Strength is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Weighted Friction Angle given Factor of Safety with respect to Shear Strength can be measured.

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Weighted Friction Angle given Factor of Safety with respect to Shear Strength Formula

​GoWeighted Friction Angle given Mobilised Friction Angle Formula

​GoWeighted Friction Angle given Submerged Unit Weight Formula

Weighted Friction Angle given Factor of Safety with respect to Shear Strength Example

Weighted Friction Angle given Factor of Safety with respect to Shear Strength Solution

Weighted Friction Angle given Factor of Safety with respect to Shear Strength Formula Elements

Other Formulas to find Weighted Friction Angle

Other formulas in Taylor's Stability Number and Stability Curves category

How to Evaluate Weighted Friction Angle given Factor of Safety with respect to Shear Strength?

FAQs on Weighted Friction Angle given Factor of Safety with respect to Shear Strength

Variable Name

GoWeighted Friction Angle given Mobilised Friction Angle Formula

GoWeighted Friction Angle given Submerged Unit Weight Formula