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Saturated Unit Weight given Normal Stress Component Formula

GoSaturated Unit Weight given Weight of Soil Prism Formula

GoSaturated Unit Weight given Vertical Stress on Prism Formula

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

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

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

Saturated Unit Weight given Normal Stress Component Example

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

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

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

25.7965 = \frac{77.36}{3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

25.7965kN/m³ = \frac{77.36kN/m²}{3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

25.7965 = \frac{77.36}{3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

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Saturated Unit Weight given Normal Stress Component Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

γ saturated = \frac{77.36kN/m²}{3m \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}}

Next Step Substitute values of Constants

∴

γ saturated = \frac{77.36kN/m²}{3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

Next Step Convert Units

∴

γ saturated = \frac{77360Pa}{3m \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}}

Next Step Prepare to Evaluate

∴

γ saturated = \frac{77360}{3 \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}}

Next Step Evaluate

∴

γ saturated = 25796.4700204889N/m³

Next Step Convert to Output's Unit

∴

γ saturated = 25.7964700204889kN/m³

LAST Step Rounding Answer

∴

γ saturated = 25.7965kN/m³

Saturated Unit Weight given Normal Stress Component Formula Elements

Variables

Constants

Functions

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

Normal Stress in Soil Mechanics

Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force.

Symbol: σ_n

Measurement: StressUnit: kN/m²

Note: Value can be positive or negative.

Formulas to find Normal Stress in Soil Mechanics

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 Saturated Unit Weight of Soil

Go Saturated Unit Weight given Weight of Soil Prism

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

Go Saturated Unit Weight given Vertical Stress on Prism

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

Go Saturated Unit Weight given Shear Stress Component

γ saturated = \frac{ζ soil}{z \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180})}

Go Saturated Unit Weight given Effective Normal Stress

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

Other formulas in Factor of Steady Seepage Along the Slope category

Go Depth of Prism given Saturated Unit Weight

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

Go Angle of Inclination given Saturated Unit Weight

i = a \cos (\frac{W prism}{γ \cdot z \cdot b})

Go Depth of Prism given Vertical Stress and Saturated Unit Weight

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

Go Angle of Inclination given Vertical Stress and Saturated Unit Weight

i = a \cos (\frac{σ z}{γ \cdot z})

How to Evaluate Saturated Unit Weight given Normal Stress Component?

Saturated Unit Weight given Normal Stress Component evaluator uses Saturated Unit Weight of Soil = Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to evaluate the Saturated Unit Weight of Soil, The Saturated Unit Weight given Normal Stress Component is defined as the value of saturated unit weight when we have prior information of other parameters used. Saturated Unit Weight of Soil is denoted by γ_saturated symbol.

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

FAQs on Saturated Unit Weight given Normal Stress Component

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

The formula of Saturated Unit Weight given Normal Stress Component is expressed as Saturated Unit Weight of Soil = Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- 0.012458 = 77360/(3*(cos((1.11701072127616*pi)/180))^2).

How to calculate Saturated Unit Weight given Normal Stress Component?

With Normal Stress in Soil Mechanics (σ_n), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) we can find Saturated Unit Weight given Normal Stress Component using the formula - Saturated Unit Weight of Soil = Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). This formula also uses Archimedes' constant and Cosine function(s).

What are the other ways to Calculate Saturated Unit Weight of Soil?

Here are the different ways to Calculate Saturated Unit Weight of Soil-

Saturated Unit Weight of Soil=Weight of Prism in Soil Mechanics/(Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight of Soil=Vertical Stress at a Point in Kilopascal/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight of Soil=Shear Stress in Soil Mechanics/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))

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

No, the Saturated Unit Weight given Normal Stress Component, measured in Specific Weight cannot be negative.

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

Saturated Unit Weight given Normal Stress Component is usually measured using the Kilonewton per Cubic Meter[kN/m³] for Specific Weight. Newton per Cubic Meter[kN/m³], Newton per Cubic Centimeter[kN/m³], Newton per Cubic Millimeter[kN/m³] are the few other units in which Saturated Unit Weight given Normal Stress Component can be measured.

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Saturated Unit Weight given Normal Stress Component Formula

​GoSaturated Unit Weight given Weight of Soil Prism Formula

​GoSaturated Unit Weight given Vertical Stress on Prism Formula

Saturated Unit Weight given Normal Stress Component Example

Saturated Unit Weight given Normal Stress Component Solution

Saturated Unit Weight given Normal Stress Component Formula Elements

Other Formulas to find Saturated Unit Weight of Soil

Other formulas in Factor of Steady Seepage Along the Slope category

How to Evaluate Saturated Unit Weight given Normal Stress Component?

FAQs on Saturated Unit Weight given Normal Stress Component

Variable Name

GoSaturated Unit Weight given Weight of Soil Prism Formula

GoSaturated Unit Weight given Vertical Stress on Prism Formula