FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Effective Normal Stress given Factor of Safety Formula

GoEffective Normal Stress given Upward Force due to Seepage Water Formula

GoEffective Normal Stress given Submerged Unit Weight Formula

Fx Copy

LaTeX Copy

Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure. Check FAQs

σ' = \frac{F s}{\frac{\tan (\frac{Φ i \cdot π}{180})}{ζ soil}}

σ^' - Effective Normal Stress in Soil Mechanics?F_s - Factor of Safety in Soil Mechanics?Φ_i - Angle of Internal Friction of Soil?ζ_soil - Shear Stress in Soil Mechanics?π - Archimedes' constant?

Effective Normal Stress given Factor of Safety Example

With values

With units

Only example

Here is how the Effective Normal Stress given Factor of Safety equation looks like with Values.

Here is how the Effective Normal Stress given Factor of Safety equation looks like with Units.

Here is how the Effective Normal Stress given Factor of Safety equation looks like.

78.7358 = \frac{2.8}{\frac{\tan (\frac{82.87 \cdot 3.1416}{180})}{0.71}}

78.7358kN/m² = \frac{2.8}{\frac{\tan (\frac{82.87° \cdot 3.1416}{180})}{0.71kN/m²}}

78.7358 = \frac{2.8}{\frac{\tan (\frac{82.87 \cdot 3.1416}{180})}{0.71}}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Civil » Category

Geotechnical Engineering » fx Effective Normal Stress given Factor of Safety

Effective Normal Stress given Factor of Safety Solution

Follow our step by step solution on how to calculate Effective Normal Stress given Factor of Safety?

FIRST Step Consider the formula

σ' = \frac{F s}{\frac{\tan (\frac{Φ i \cdot π}{180})}{ζ soil}}

Next Step Substitute values of Variables

∴

σ' = \frac{2.8}{\frac{\tan (\frac{82.87° \cdot π}{180})}{0.71kN/m²}}

Next Step Substitute values of Constants

∴

σ' = \frac{2.8}{\frac{\tan (\frac{82.87° \cdot 3.1416}{180})}{0.71kN/m²}}

Next Step Convert Units

∴

σ' = \frac{2.8}{\frac{\tan (\frac{1.4464rad \cdot 3.1416}{180})}{710Pa}}

Next Step Prepare to Evaluate

∴

σ' = \frac{2.8}{\frac{\tan (\frac{1.4464 \cdot 3.1416}{180})}{710}}

Next Step Evaluate

∴

σ' = 78735.7633090358Pa

Next Step Convert to Output's Unit

∴

σ' = 78.7357633090358kN/m²

LAST Step Rounding Answer

∴

σ' = 78.7358kN/m²

Effective Normal Stress given Factor of Safety Formula Elements

Variables

Constants

Functions

Effective Normal Stress in Soil Mechanics

Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.

Symbol: σ^'

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Effective Normal Stress in Soil Mechanics

Factor of Safety in Soil Mechanics

Factor of Safety in Soil Mechanics 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 in Soil Mechanics

Angle of Internal Friction of Soil

Angle of Internal Friction of Soil is 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

Shear Stress in Soil Mechanics

Shear Stress in Soil Mechanics is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: ζ_soil

Measurement: StressUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Shear Stress 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 Effective Normal Stress in Soil Mechanics

Go Effective Normal Stress given Upward Force due to Seepage Water

σ' = σ n - F u

Go Effective Normal Stress given Submerged Unit Weight

σ' = (y S \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

Go Effective Normal Stress given Saturated Unit Weight

σ' = ((γ saturated - γ water) \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

Other formulas in Steady State Seepage Analysis Along The Slopes category

Go Weight of Soil Prism given Saturated Unit Weight

W prism = (γ saturated \cdot z \cdot b \cdot \cos (\frac{i \cdot π}{180}))

Go Inclined Length of Prism given Saturated Unit Weight

b = \frac{W prism}{γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180})}

Go Vertical Stress on Prism given Saturated Unit Weight

σ zkp = (γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}))

Go Normal Stress Component given Saturated Unit Weight

σ n = (γ saturated \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

How to Evaluate Effective Normal Stress given Factor of Safety?

Effective Normal Stress given Factor of Safety evaluator uses Effective Normal Stress in Soil Mechanics = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics) to evaluate the Effective Normal Stress in Soil Mechanics, The Effective Normal Stress given Factor of Safety is defined as the value of effective normal stress when we have prior information of other parameters used. Effective Normal Stress in Soil Mechanics is denoted by σ^' symbol.

How to evaluate Effective Normal Stress given Factor of Safety using this online evaluator? To use this online evaluator for Effective Normal Stress given Factor of Safety, enter Factor of Safety in Soil Mechanics (F_s), Angle of Internal Friction of Soil (Φ_i) & Shear Stress in Soil Mechanics (ζ_soil) and hit the calculate button.

FAQs on Effective Normal Stress given Factor of Safety

What is the formula to find Effective Normal Stress given Factor of Safety?

The formula of Effective Normal Stress given Factor of Safety is expressed as Effective Normal Stress in Soil Mechanics = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics). Here is an example- 0.078736 = 2.8/((tan((1.44635435112743*pi)/180))/710).

How to calculate Effective Normal Stress given Factor of Safety?

With Factor of Safety in Soil Mechanics (F_s), Angle of Internal Friction of Soil (Φ_i) & Shear Stress in Soil Mechanics (ζ_soil) we can find Effective Normal Stress given Factor of Safety using the formula - Effective Normal Stress in Soil Mechanics = Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics). This formula also uses Archimedes' constant and Tangent (tan) function(s).

What are the other ways to Calculate Effective Normal Stress in Soil Mechanics?

Here are the different ways to Calculate Effective Normal Stress in Soil Mechanics-

Effective Normal Stress in Soil Mechanics=Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis
Effective Normal Stress in Soil Mechanics=(Submerged Unit Weight in KN per Cubic Meter*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Effective Normal Stress in Soil Mechanics=((Saturated Unit Weight of Soil-Unit Weight of Water)*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Can the Effective Normal Stress given Factor of Safety be negative?

No, the Effective Normal Stress given Factor of Safety, measured in Pressure cannot be negative.

Which unit is used to measure Effective Normal Stress given Factor of Safety?

Effective Normal Stress given Factor of Safety is usually measured using the Kilonewton per Square Meter[kN/m²] for Pressure. Pascal[kN/m²], Kilopascal[kN/m²], Bar[kN/m²] are the few other units in which Effective Normal Stress given Factor of Safety can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

Effective Normal Stress given Factor of Safety Formula

​GoEffective Normal Stress given Upward Force due to Seepage Water Formula

​GoEffective Normal Stress given Submerged Unit Weight Formula

Effective Normal Stress given Factor of Safety Example

Effective Normal Stress given Factor of Safety Solution

Effective Normal Stress given Factor of Safety Formula Elements

Other Formulas to find Effective Normal Stress in Soil Mechanics

Other formulas in Steady State Seepage Analysis Along The Slopes category

How to Evaluate Effective Normal Stress given Factor of Safety?

FAQs on Effective Normal Stress given Factor of Safety

Variable Name

GoEffective Normal Stress given Upward Force due to Seepage Water Formula

GoEffective Normal Stress given Submerged Unit Weight Formula