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Unit Weight of Soil given Normal Stress Component Formula

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Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil. Check FAQs

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

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

Unit Weight of Soil given Normal Stress Component Example

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

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

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

16.673 = \frac{50}{3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

16.673kN/m³ = \frac{50kPa}{3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

16.673 = \frac{50}{3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

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Unit Weight of Soil given Normal Stress Component Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

γ = \frac{50kPa}{3m \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}}

Next Step Substitute values of Constants

∴

γ = \frac{50kPa}{3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

Next Step Convert Units

∴

γ = \frac{50000Pa}{3m \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}}

Next Step Prepare to Evaluate

∴

γ = \frac{50000}{3 \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}}

Next Step Evaluate

∴

γ = 16673.0028570895N/m³

Next Step Convert to Output's Unit

∴

γ = 16.6730028570895kN/m³

LAST Step Rounding Answer

∴

γ = 16.673kN/m³

Unit Weight of Soil given Normal Stress Component Formula Elements

Variables

Constants

Functions

Unit Weight of Soil

Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

Symbol: γ

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Soil

Normal Stress in kp

Normal Stress in kp is defined as the stress produced by the perpendicular action of a force on a given area in kilopascal.

Symbol: σ_n

Measurement: PressureUnit: kPa

Note: Value should be greater than 0.

Formulas to find Normal Stress in kp

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 in Normal Stress Component category

Go Normal Stress Component given Vertical Stress

σ n = σ zkp \cdot \cos (\frac{i \cdot π}{180})

Go Vertical Stress on Surface of Prism given Normal Stress Component

σ zkp = \frac{σ n}{\cos (\frac{i \cdot π}{180})}

Go Angle of Inclination given Normal Stress Component

i = a \cos (\frac{σ n}{σ zkp})

Go Normal Stress Component given Unit Weight of Soil

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

How to Evaluate Unit Weight of Soil given Normal Stress Component?

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

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

FAQs on Unit Weight of Soil given Normal Stress Component

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

The formula of Unit Weight of Soil given Normal Stress Component is expressed as Unit Weight of Soil = Normal Stress in kp/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- 0.017673 = 50000/(3*(cos((1.11701072127616*pi)/180))^2).

How to calculate Unit Weight of Soil given Normal Stress Component?

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

Can the Unit Weight of Soil given Normal Stress Component be negative?

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

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

Unit Weight of Soil 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 Unit Weight of Soil given Normal Stress Component can be measured.

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Unit Weight of Soil given Normal Stress Component Formula

Unit Weight of Soil given Normal Stress Component Example

Unit Weight of Soil given Normal Stress Component Solution

Unit Weight of Soil given Normal Stress Component Formula Elements

Other formulas in Normal Stress Component category

How to Evaluate Unit Weight of Soil given Normal Stress Component?

FAQs on Unit Weight of Soil given Normal Stress Component

Variable Name