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Effective Normal Stress given Saturated Unit Weight Formula

GoEffective Normal Stress given Upward Force due to Seepage Water Formula

GoEffective Normal Stress given Submerged Unit Weight Formula

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

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

σ^' - Effective Normal Stress in Soil Mechanics?γ_saturated - Saturated Unit Weight of Soil?γ_water - Unit Weight of Water?z - Depth of Prism?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Effective Normal Stress given Saturated Unit Weight Example

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Here is how the Effective Normal Stress given Saturated Unit Weight equation looks like with Values.

Here is how the Effective Normal Stress given Saturated Unit Weight equation looks like with Units.

Here is how the Effective Normal Stress given Saturated Unit Weight equation looks like.

6.2376 = ((11.89 - 9.81) \cdot 3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})

6.2376kN/m² = ((11.89kN/m³ - 9.81kN/m³) \cdot 3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})

6.2376 = ((11.89 - 9.81) \cdot 3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2})

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Effective Normal Stress given Saturated Unit Weight Solution

Follow our step by step solution on how to calculate Effective Normal Stress given Saturated Unit Weight?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ' = ((11.89kN/m³ - 9.81kN/m³) \cdot 3m \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2})

Next Step Substitute values of Constants

∴

σ' = ((11.89kN/m³ - 9.81kN/m³) \cdot 3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2})

Next Step Convert Units

∴

σ' = ((11890N/m³ - 9810N/m³) \cdot 3m \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2})

Next Step Prepare to Evaluate

∴

σ' = ((11890 - 9810) \cdot 3 \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2})

Next Step Evaluate

∴

σ' = 6237.6286318321Pa

Next Step Convert to Output's Unit

∴

σ' = 6.2376286318321kN/m²

LAST Step Rounding Answer

∴

σ' = 6.2376kN/m²

Effective Normal Stress given Saturated Unit Weight 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

Saturated Unit Weight of Soil

Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.

Symbol: γ_saturated

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Saturated Unit Weight of Soil

Unit Weight of Water

Unit Weight of Water is mass per unit of water.

Symbol: γ_water

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Water

Depth of Prism

Depth of Prism is the length of prism along z direction.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Prism

Angle of Inclination to Horizontal in Soil

Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

Symbol: i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination to Horizontal in Soil

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(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 Factor of Safety

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

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 Saturated Unit Weight?

Effective Normal Stress given Saturated Unit Weight evaluator uses 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) to evaluate the Effective Normal Stress in Soil Mechanics, The Effective Normal Stress given Saturated Unit Weight 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 Saturated Unit Weight using this online evaluator? To use this online evaluator for Effective Normal Stress given Saturated Unit Weight, enter Saturated Unit Weight of Soil (γ_saturated), Unit Weight of Water (γ_water), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Effective Normal Stress given Saturated Unit Weight

What is the formula to find Effective Normal Stress given Saturated Unit Weight?

The formula of Effective Normal Stress given Saturated Unit Weight is expressed as 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). Here is an example- 0.024561 = ((11890-9810)*3*(cos((1.11701072127616*pi)/180))^2).

How to calculate Effective Normal Stress given Saturated Unit Weight?

With Saturated Unit Weight of Soil (γ_saturated), Unit Weight of Water (γ_water), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) we can find Effective Normal Stress given Saturated Unit Weight using the formula - 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). This formula also uses Archimedes' constant and Cosine (cos) 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=Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/Shear Stress in Soil Mechanics)

Can the Effective Normal Stress given Saturated Unit Weight be negative?

No, the Effective Normal Stress given Saturated Unit Weight, measured in Pressure cannot be negative.

Which unit is used to measure Effective Normal Stress given Saturated Unit Weight?

Effective Normal Stress given Saturated Unit Weight 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 Saturated Unit Weight can be measured.

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Effective Normal Stress given Saturated Unit Weight Formula

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

​GoEffective Normal Stress given Submerged Unit Weight Formula

Effective Normal Stress given Saturated Unit Weight Example

Effective Normal Stress given Saturated Unit Weight Solution

Effective Normal Stress given Saturated Unit Weight 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 Saturated Unit Weight?

FAQs on Effective Normal Stress given Saturated Unit Weight

Variable Name

GoEffective Normal Stress given Upward Force due to Seepage Water Formula

GoEffective Normal Stress given Submerged Unit Weight Formula