Submerged Unit Weight given Normal Stress Component Calculator

✖Normal stress is defined as the stress produced by the perpendicular action of a force on a given area.ⓘ Normal Stress [σ_Normal]			+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%

✖Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.ⓘ Submerged Unit Weight given Normal Stress Component [γ^']

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Formula

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Submerged Unit Weight given Normal Stress Component

Formula

`"γ"^{"'"} = "σ"_{"Normal"}/("z"*(cos(("i")))^2)`

Example

`"1.387666N/m³"="0.8Pa"/("3m"*(cos(("64°")))^2)`

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Submerged Unit Weight given Normal Stress Component Solution

STEP 0: Pre-Calculation Summary

Formula Used

Submerged Unit Weight = Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2)
γ^' = σ_Normal/(z*(cos((i)))^2)
This formula uses 1 Functions, 4 Variables

Functions Used

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

Submerged Unit Weight - (Measured in Newton per Cubic Meter) - Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.
Normal Stress - (Measured in Pascal) - Normal stress is defined as the stress produced by the perpendicular action of a force on a given area.
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

Normal Stress: 0.8 Pascal --> 0.8 Pascal No Conversion Required
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^' = σ_Normal/(z*(cos((i)))^2) --> 0.8/(3*(cos((1.11701072127616)))^2)

Evaluating ... ...

γ^' = 1.38766555807742

STEP 3: Convert Result to Output's Unit

1.38766555807742 Newton per Cubic Meter --> No Conversion Required

FINAL ANSWER

1.38766555807742 ≈ 1.387666 Newton per Cubic Meter <-- Submerged Unit Weight

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< 14 Stability Analysis Of Submerged Slopes Calculators

Cohesion given Submerged Unit Weight

Go Cohesion of Soil = (Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination to Horizontal in Soil))))*(Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Submerged Unit Weight given Factor of Safety for Cohesive Soil

Go Submerged Unit Weight = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))

Depth of Prism for Cohesive Soil given Submerged Slope

Go Depth of Prism = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))

Factor of Safety for Cohesive Soil given Depth of Prism

Go Factor of Safety = (Cohesion of Soil/(Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))+(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil)))

Angle of Internal Friction given Factor of Safety for Submerged Slope

Go Angle of Internal Friction of Soil = atan(tan((Angle of Inclination to Horizontal in Soil))*(Factor of Safety-(Cohesion in Soil as Kilopascal/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))))

Cohesion of Soil given Submerged Unit Weight

Go Cohesion of Soil = Critical Depth/(((sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction)))))

Critical Depth given Submerged Unit Weight

Go Critical Depth = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction))))

Submerged Unit Weight given Critical Depth

Go Submerged Unit Weight = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Critical Depth*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction))))

Depth of Prism given Submerged Unit Weight and Shear Stress

Go Depth of Prism = Shear Stress for Submerged Slopes/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Shear Stress Component given Submerged Unit Weight

Go Shear Stress for Submerged Slopes = (Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Submerged Unit Weight given Shear Stress Component

Go Submerged Unit Weight = Shear Stress for Submerged Slopes/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Submerged Unit Weight given Normal Stress Component

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

Depth of Prism given Submerged Unit Weight

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

Normal Stress Component given Submerged Unit Weight

Go Normal Stress = Submerged Unit Weight*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2

Submerged Unit Weight given Normal Stress Component Formula

Submerged Unit Weight = Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2)
γ^' = σ_Normal/(z*(cos((i)))^2)

What is Submerged Unit Weight?

The weight of the solids in air minus the weight of water displaced by the solids per unit of volume of soil mass; the saturated unit weight minus the unit weight of water.

How to Calculate Submerged Unit Weight given Normal Stress Component?

Submerged Unit Weight given Normal Stress Component calculator uses Submerged Unit Weight = Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2) to calculate the Submerged Unit Weight, The Submerged Unit Weight given Normal Stress Component is defined as force per unit volume of soil beneath the water table, part of the normal stress component. Submerged Unit Weight is denoted by γ^' symbol.

How to calculate Submerged Unit Weight given Normal Stress Component using this online calculator? To use this online calculator for Submerged Unit Weight given Normal Stress Component, enter Normal Stress (σ_Normal), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Submerged Unit Weight given Normal Stress Component calculation can be explained with given input values -> 1.387666 = 0.8/(3*(cos((1.11701072127616)))^2).

FAQ

What is Submerged Unit Weight given Normal Stress Component?

The Submerged Unit Weight given Normal Stress Component is defined as force per unit volume of soil beneath the water table, part of the normal stress component and is represented as γ^' = σ_Normal/(z*(cos((i)))^2) or Submerged Unit Weight = Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2). Normal stress is defined as the stress produced by the perpendicular action of a force on a given area, 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 Submerged Unit Weight given Normal Stress Component?

The Submerged Unit Weight given Normal Stress Component is defined as force per unit volume of soil beneath the water table, part of the normal stress component is calculated using Submerged Unit Weight = Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2). To calculate Submerged Unit Weight given Normal Stress Component, you need Normal Stress (σ_Normal), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Normal Stress, 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 Submerged Unit Weight?

In this formula, Submerged Unit Weight uses Normal Stress, Depth of Prism & Angle of Inclination to Horizontal in Soil. We can use 3 other way(s) to calculate the same, which is/are as follows -

Submerged Unit Weight = Shear Stress for Submerged Slopes/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))
Submerged Unit Weight = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))
Submerged Unit Weight = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Critical Depth*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction))))

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