Shear Stress Component given Submerged Unit Weight Calculator

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

✖Shear Stress for Submerged Slopes is the force per unit area parallel to the slope surface beneath water, causing deformation.ⓘ Shear Stress Component given Submerged Unit Weight [𝜏]

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Formula

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Shear Stress Component given Submerged Unit Weight

Formula

`"𝜏" = ("γ"^{"'"}*"z"*cos(("i"))*sin(("i")))`

Example

`"5.921901Pa"=("5.01N/m³"*"3m"*cos(("64°"))*sin(("64°")))`

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Shear Stress Component given Submerged Unit Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
𝜏 = (γ^'*z*cos((i))*sin((i)))
This formula uses 2 Functions, 4 Variables

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

Shear Stress for Submerged Slopes - (Measured in Pascal) - Shear Stress for Submerged Slopes is the force per unit area parallel to the slope surface beneath water, causing deformation.
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.
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

Submerged Unit Weight: 5.01 Newton per Cubic Meter --> 5.01 Newton per Cubic Meter 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

𝜏 = (γ^'*z*cos((i))*sin((i))) --> (5.01*3*cos((1.11701072127616))*sin((1.11701072127616)))

Evaluating ... ...

𝜏 = 5.92190081335647

STEP 3: Convert Result to Output's Unit

5.92190081335647 Pascal --> No Conversion Required

FINAL ANSWER

5.92190081335647 ≈ 5.921901 Pascal <-- Shear Stress for Submerged Slopes

(Calculation completed in 00.020 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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

Shear Stress Component given Submerged Unit Weight Formula

What is Shear Stress?

Shear stress, often denoted by τ (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand.

How to Calculate Shear Stress Component given Submerged Unit Weight?

Shear Stress Component given Submerged Unit Weight calculator uses 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))) to calculate the Shear Stress for Submerged Slopes, The Shear Stress Component given Submerged Unit Weight is defined as the force per unit volume acting vertically; shear stress component is its horizontal counterpart in soil mechanics. Shear Stress for Submerged Slopes is denoted by 𝜏 symbol.

How to calculate Shear Stress Component given Submerged Unit Weight using this online calculator? To use this online calculator for Shear Stress Component given Submerged Unit Weight, enter Submerged Unit Weight (γ^'), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Shear Stress Component given Submerged Unit Weight calculation can be explained with given input values -> 5.910081 = (5.01*3*cos((1.11701072127616))*sin((1.11701072127616))).

FAQ

What is Shear Stress Component given Submerged Unit Weight?

The Shear Stress Component given Submerged Unit Weight is defined as the force per unit volume acting vertically; shear stress component is its horizontal counterpart in soil mechanics and is represented as 𝜏 = (γ^'*z*cos((i))*sin((i))) or 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 is the unit weight of weight of soil as observed underwater in a saturated condition of course, 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 Shear Stress Component given Submerged Unit Weight?

The Shear Stress Component given Submerged Unit Weight is defined as the force per unit volume acting vertically; shear stress component is its horizontal counterpart in soil mechanics is calculated using 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))). To calculate Shear Stress Component given Submerged Unit Weight, you need Submerged Unit Weight (γ^'), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Submerged Unit Weight, 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.

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