Saturated Unit Weight given Shear Stress Component Calculator

✖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.ⓘ Shear Stress in Soil Mechanics [ζ_soil]			+10% -10%
✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism [z]			+10% -10%
✖Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination to Horizontal in Soil [i]			+10% -10%

✖Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.ⓘ Saturated Unit Weight given Shear Stress Component [γ_saturated]

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Saturated Unit Weight given Shear Stress Component

Formula

`"γ"_{"saturated"} = "ζ"_{"soil"}/("z"*cos(("i"*pi)/180)*sin(("i"*pi)/180))`

Example

`"12.14262kN/m³"="0.71kN/m²"/("3m"*cos(("64°"*pi)/180)*sin(("64°"*pi)/180))`

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Saturated Unit Weight given Shear Stress Component Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
γ_saturated = ζ_soil/(z*cos((i*pi)/180)*sin((i*pi)/180))
This formula uses 1 Constants, 2 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Saturated Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.
Shear Stress in Soil Mechanics - (Measured in Pascal) - 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.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Angle of Inclination to Horizontal in Soil - (Measured in Radian) - Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

STEP 1: Convert Input(s) to Base Unit

Shear Stress in Soil Mechanics: 0.71 Kilonewton per Square Meter --> 710 Pascal (Check conversion here)
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

γ_saturated = ζ_soil/(z*cos((i*pi)/180)*sin((i*pi)/180)) --> 710/(3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180))

Evaluating ... ...

γ_saturated = 12142.6208198275

STEP 3: Convert Result to Output's Unit

12142.6208198275 Newton per Cubic Meter -->12.1426208198275 Kilonewton per Cubic Meter (Check conversion here)

FINAL ANSWER

12.1426208198275 ≈ 12.14262 Kilonewton per Cubic Meter <-- Saturated Unit Weight of Soil

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 18 Factor of Steady Seepage Along the Slope Calculators

Saturated Unit Weight given Shear Strength

Go Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*Shear Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))/(Shear Strength in KN per Cubic Meter*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Saturated Unit Weight given Factor of Safety

Go Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

Depth of Prism given Shear Stress and Saturated Unit Weight

Go 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))

Saturated Unit Weight given Shear Stress Component

Go 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))

Angle of Inclination given Shear Strength and Submerged Unit Weight

Go Angle of Inclination to Horizontal in Soil = atan((Submerged Unit Weight*tan((Angle of Internal Friction)))/(Saturated Unit Weight in Newton per Cubic Meter*(Shear Strength of Soil/Shear Stress in Soil Mechanics)))

Depth of Prism given Upward Force

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

Depth of Prism given Saturated Unit Weight

Go 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))

Saturated Unit Weight given Effective Normal Stress

Go Saturated Unit Weight of Soil = Unit Weight of Water+(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))

Depth of Prism given Effective Normal Stress

Go Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Saturated Unit Weight given Weight of Soil Prism

Go 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))

Depth of Prism given Submerged Unit Weight and Effective Normal Stress

Go Depth of Prism = Effective Normal Stress in Soil Mechanics/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Depth of Prism given Vertical Stress and Saturated Unit Weight

Go 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))

Saturated Unit Weight given Vertical Stress on Prism

Go 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))

Angle of Inclination given Saturated Unit Weight

Go Angle of Inclination to Horizontal in Soil = acos(Weight of Prism in Soil Mechanics/(Unit Weight of Soil*Depth of Prism*Inclined Length of Prism))

Depth of Prism given Normal Stress and Saturated Unit Weight

Go Depth of Prism = Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Saturated Unit Weight given Normal Stress Component

Go Saturated Unit Weight of Soil = Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Depth of Prism given Upward Force due to Seepage Water

Go Depth of Prism = Upward Force in Seepage Analysis/(Unit Weight of Water*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Angle of Inclination given Vertical Stress and Saturated Unit Weight

Go Angle of Inclination to Horizontal in Soil = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism))

Saturated Unit Weight given Shear Stress Component Formula

What is Unit Weight?

Unit weight is also known by the name specific weight. Unit weight of the soil is the total weight of the soil divided by total volume. Total weight of soil also includes weight of water. Total volume occupied includes the volume of water as well as the volume of air along with the soil volume.

How to Calculate Saturated Unit Weight given Shear Stress Component?

Saturated Unit Weight given Shear Stress Component calculator uses 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)) to calculate the Saturated Unit Weight of Soil, The Saturated Unit Weight given Shear 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 calculate Saturated Unit Weight given Shear Stress Component using this online calculator? To use this online calculator for Saturated Unit Weight given Shear Stress Component, enter Shear Stress in Soil Mechanics (ζ_soil), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Saturated Unit Weight given Shear Stress Component calculation can be explained with given input values -> 0.012143 = 710/(3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180)).

FAQ

What is Saturated Unit Weight given Shear Stress Component?

The Saturated Unit Weight given Shear Stress Component is defined as the value of saturated unit weight when we have prior information of other parameters used and is represented as γ_saturated = ζ_soil/(z*cos((i*pi)/180)*sin((i*pi)/180)) or 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)). 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, Depth of Prism is the length of prism along z direction & Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

How to calculate Saturated Unit Weight given Shear Stress Component?

The Saturated Unit Weight given Shear Stress Component is defined as the value of saturated unit weight when we have prior information of other parameters used is calculated using 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)). To calculate Saturated Unit Weight given Shear Stress Component, you need Shear Stress in Soil Mechanics (ζ_soil), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Shear Stress in Soil Mechanics, Depth of Prism & Angle of Inclination to Horizontal in Soil and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Saturated Unit Weight of Soil?

In this formula, Saturated Unit Weight of Soil uses Shear Stress in Soil Mechanics, Depth of Prism & Angle of Inclination to Horizontal in Soil. We can use 6 other way(s) to calculate the same, which is/are as follows -

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 = Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Saturated Unit Weight of Soil = Unit Weight of Water+(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))
Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*Shear Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))/(Shear Strength in KN per Cubic Meter*tan((Angle of Inclination to Horizontal in Soil*pi)/180))

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