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Factor of Safety with respect to Shear Strength Formula

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

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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. Check FAQs

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

f_s - Factor of Safety?γ^' - Submerged Unit Weight?γ_sat - Saturated Unit Weight?φ - Angle of Internal Friction?φ_IF - Weighted Friction Angle for Internal Friction?

Factor of Safety with respect to Shear Strength Example

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

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

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

2.7976 = ((\frac{31}{9.98}) \cdot (\frac{\tan ((9.93))}{\tan ((11))}))

2.7976 = ((\frac{31N/m³}{9.98N/m³}) \cdot (\frac{\tan ((9.93°))}{\tan ((11°))}))

2.7976 = ((\frac{31}{9.98}) \cdot (\frac{\tan ((9.93))}{\tan ((11))}))

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Factor of Safety with respect to Shear Strength Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

f s = ((\frac{31N/m³}{9.98N/m³}) \cdot (\frac{\tan ((9.93°))}{\tan ((11°))}))

Next Step Convert Units

∴

f s = ((\frac{31N/m³}{9.98N/m³}) \cdot (\frac{\tan ((0.1733rad))}{\tan ((0.192rad))}))

Next Step Prepare to Evaluate

∴

f s = ((\frac{31}{9.98}) \cdot (\frac{\tan ((0.1733))}{\tan ((0.192))}))

Next Step Evaluate

∴

f s = 2.79759280892602

LAST Step Rounding Answer

∴

f s = 2.7976

Factor of Safety with respect to Shear Strength Formula Elements

Variables

Functions

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

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

Angle of Internal Friction is the angle measured between the normal force and resultant force.

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Internal Friction

Weighted Friction Angle for Internal Friction

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

Symbol: φ_IF

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Weighted Friction Angle for Internal Friction

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 with respect to Shear Strength given Weighted Friction Angle

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

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

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

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

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 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 Factor of Safety with respect to Shear Strength?

Factor of Safety with respect to Shear Strength evaluator uses Factor of Safety = ((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction))/tan((Weighted Friction Angle for Internal Friction)))) to evaluate the Factor of Safety, The Factor of Safety with respect to Shear Strength formula is defined as the value of a measure of the load-carrying capacity of a structure or material compared to the actual load or stress that is applied to it, when we have prior information of other parameters used. Factor of Safety is denoted by f_s symbol.

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

FAQs on Factor of Safety with respect to Shear Strength

What is the formula to find Factor of Safety with respect to Shear Strength?

The formula of Factor of Safety with respect to Shear Strength is expressed as Factor of Safety = ((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction))/tan((Weighted Friction Angle for Internal Friction)))). Here is an example- 16.54785 = ((31/9.98)*(tan((0.173311194723004))/tan((0.19198621771934)))).

How to calculate Factor of Safety with respect to Shear Strength?

With Submerged Unit Weight (γ^'), Saturated Unit Weight (γ_sat), Angle of Internal Friction (φ) & Weighted Friction Angle for Internal Friction (φ_IF) we can find Factor of Safety with respect to Shear Strength using the formula - Factor of Safety = ((Submerged Unit Weight/Saturated Unit Weight)*(tan((Angle of Internal Friction))/tan((Weighted Friction Angle for Internal Friction)))). This formula also uses Tangent (tan) 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=(Submerged Unit Weight*Effective Angle of Internal Friction)/(Weighted Friction Angle for Internal Friction*Saturated Unit Weight)

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Factor of Safety with respect to Shear Strength Formula

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

Factor of Safety with respect to Shear Strength Example

Factor of Safety with respect to Shear Strength Solution

Factor of Safety with respect to Shear Strength Formula Elements

Other Formulas to find Factor of Safety

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

How to Evaluate Factor of Safety with respect to Shear Strength?

FAQs on Factor of Safety with respect to Shear Strength

Variable Name

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