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Depth of Prism given Shear Stress and Saturated Unit Weight Formula

GoDepth of Prism given Saturated Unit Weight Formula

GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula

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

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

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

Depth of Prism given Shear Stress and Saturated Unit Weight Example

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Here is how the Depth of Prism given Shear Stress and Saturated Unit Weight equation looks like with Values.

Here is how the Depth of Prism given Shear Stress and Saturated Unit Weight equation looks like with Units.

Here is how the Depth of Prism given Shear Stress and Saturated Unit Weight equation looks like.

3.0637 = \frac{0.71}{11.89 \cdot \cos (\frac{64 \cdot 3.1416}{180}) \cdot \sin (\frac{64 \cdot 3.1416}{180})}

3.0637m = \frac{0.71kN/m²}{11.89kN/m³ \cdot \cos (\frac{64° \cdot 3.1416}{180}) \cdot \sin (\frac{64° \cdot 3.1416}{180})}

3.0637 = \frac{0.71}{11.89 \cdot \cos (\frac{64 \cdot 3.1416}{180}) \cdot \sin (\frac{64 \cdot 3.1416}{180})}

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Depth of Prism given Shear Stress and Saturated Unit Weight Solution

Follow our step by step solution on how to calculate Depth of Prism given Shear Stress and Saturated Unit Weight?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

z = \frac{0.71kN/m²}{11.89kN/m³ \cdot \cos (\frac{64° \cdot π}{180}) \cdot \sin (\frac{64° \cdot π}{180})}

Next Step Substitute values of Constants

∴

z = \frac{0.71kN/m²}{11.89kN/m³ \cdot \cos (\frac{64° \cdot 3.1416}{180}) \cdot \sin (\frac{64° \cdot 3.1416}{180})}

Next Step Convert Units

∴

z = \frac{710Pa}{11890N/m³ \cdot \cos (\frac{1.117rad \cdot 3.1416}{180}) \cdot \sin (\frac{1.117rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

z = \frac{710}{11890 \cdot \cos (\frac{1.117 \cdot 3.1416}{180}) \cdot \sin (\frac{1.117 \cdot 3.1416}{180})}

Next Step Evaluate

∴

z = 3.06373948355613m

LAST Step Rounding Answer

∴

z = 3.0637m

Depth of Prism given Shear Stress and Saturated Unit Weight Formula Elements

Variables

Constants

Functions

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

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

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

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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 Depth of Prism

Go Depth of Prism given Saturated Unit Weight

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

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 Depth of Prism given Normal Stress and Saturated Unit Weight

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

Go Depth of Prism given Upward Force due to Seepage Water

z = \frac{F u}{γ water \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Other formulas in Factor of Steady Seepage Along the Slope category

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 Angle of Inclination given Saturated Unit Weight

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

Go Saturated Unit Weight given Vertical Stress on Prism

γ saturated = \frac{σ zkp}{z \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 Depth of Prism given Shear Stress and Saturated Unit Weight?

Depth of Prism given Shear Stress and Saturated Unit Weight evaluator uses Depth of Prism = Shear Stress in Soil Mechanics/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180)) to evaluate the Depth of Prism, Depth of Prism given Shear Stress and Saturated Unit Weight calculates value of depth of prism when we have prior information of other parameters used. Depth of Prism is denoted by z symbol.

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

FAQs on Depth of Prism given Shear Stress and Saturated Unit Weight

What is the formula to find Depth of Prism given Shear Stress and Saturated Unit Weight?

The formula of Depth of Prism given Shear Stress and Saturated Unit Weight is expressed as Depth of Prism = Shear Stress in Soil Mechanics/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180)). Here is an example- 3.063739 = 710/(11890*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180)).

How to calculate Depth of Prism given Shear Stress and Saturated Unit Weight?

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

What are the other ways to Calculate Depth of Prism?

Here are the different ways to Calculate Depth of Prism-

Depth of Prism=Weight of Prism in Soil Mechanics/(Saturated Unit Weight in Newton per Cubic Meter*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism=Vertical Stress at a Point in Kilopascal/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism=Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Can the Depth of Prism given Shear Stress and Saturated Unit Weight be negative?

No, the Depth of Prism given Shear Stress and Saturated Unit Weight, measured in Length cannot be negative.

Which unit is used to measure Depth of Prism given Shear Stress and Saturated Unit Weight?

Depth of Prism given Shear Stress and Saturated Unit Weight is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Depth of Prism given Shear Stress and Saturated Unit Weight can be measured.

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Depth of Prism given Shear Stress and Saturated Unit Weight Formula

​GoDepth of Prism given Saturated Unit Weight Formula

​GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula

Depth of Prism given Shear Stress and Saturated Unit Weight Example

Depth of Prism given Shear Stress and Saturated Unit Weight Solution

Depth of Prism given Shear Stress and Saturated Unit Weight Formula Elements

Other Formulas to find Depth of Prism

Other formulas in Factor of Steady Seepage Along the Slope category

How to Evaluate Depth of Prism given Shear Stress and Saturated Unit Weight?

FAQs on Depth of Prism given Shear Stress and Saturated Unit Weight

Variable Name

GoDepth of Prism given Saturated Unit Weight Formula

GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula