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Shear Stress given Submerged Unit Weight Formula

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GoShear Stress Component given Saturated Unit Weight Formula

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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. Check FAQs

ζ soil = \frac{τ f}{\frac{y S \cdot \tan ((φ))}{γ saturated \cdot \tan ((i))}}

ζ_soil - Shear Stress in Soil Mechanics?τ_f - Shear Strength in KN per Cubic Meter?y_S - Submerged Unit Weight in KN per Cubic Meter?φ - Angle of Internal Friction?γ_saturated - Saturated Unit Weight of Soil?i - Angle of Inclination to Horizontal in Soil?

Shear Stress given Submerged Unit Weight Example

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With units

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Here is how the Shear Stress given Submerged Unit Weight equation looks like with Values.

Here is how the Shear Stress given Submerged Unit Weight equation looks like with Units.

Here is how the Shear Stress given Submerged Unit Weight equation looks like.

23.165 = \frac{4.92}{\frac{5 \cdot \tan ((46))}{11.89 \cdot \tan ((64))}}

23.165kN/m² = \frac{4.92kN/m²}{\frac{5kN/m³ \cdot \tan ((46°))}{11.89kN/m³ \cdot \tan ((64°))}}

23.165 = \frac{4.92}{\frac{5 \cdot \tan ((46))}{11.89 \cdot \tan ((64))}}

Tip: Use pencil () icon above to edit Input Values and Units.

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Shear Stress given Submerged Unit Weight Solution

Follow our step by step solution on how to calculate Shear Stress given Submerged Unit Weight?

FIRST Step Consider the formula

ζ soil = \frac{τ f}{\frac{y S \cdot \tan ((φ))}{γ saturated \cdot \tan ((i))}}

Next Step Substitute values of Variables

∴

ζ soil = \frac{4.92kN/m²}{\frac{5kN/m³ \cdot \tan ((46°))}{11.89kN/m³ \cdot \tan ((64°))}}

Next Step Convert Units

∴

ζ soil = \frac{4920Pa}{\frac{5000N/m³ \cdot \tan ((0.8029rad))}{11890N/m³ \cdot \tan ((1.117rad))}}

Next Step Prepare to Evaluate

∴

ζ soil = \frac{4920}{\frac{5000 \cdot \tan ((0.8029))}{11890 \cdot \tan ((1.117))}}

Next Step Evaluate

∴

ζ soil = 23165.0030463537Pa

Next Step Convert to Output's Unit

∴

ζ soil = 23.1650030463537kN/m²

LAST Step Rounding Answer

∴

ζ soil = 23.165kN/m²

Shear Stress given Submerged Unit Weight Formula Elements

Variables

Functions

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.

Shear Strength in KN per Cubic Meter

Shear Strength in KN per Cubic Meter is the strength of a material against structural failure when the material fails in shear.

Symbol: τ_f

Measurement: StressUnit: kN/m²

Note: Value should be greater than 0.

Submerged Unit Weight in KN per Cubic Meter

Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.

Symbol: y_S

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Angle of Internal Friction

Angle of Internal Friction is the angle measured between the normal force and resultant force .

Symbol: φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

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.

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.

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Credits

Creator Image

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Formula and 2100+ more formulas!

Verifier Image

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Formula and 2600+ more formulas!

Other Formulas to find Shear Stress in Soil Mechanics

Go Shear Stress Component given Saturated Unit Weight

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

Other formulas in Steady State Seepage Analysis Along The Slopes category

Go Weight of Soil Prism given Saturated Unit Weight

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

Go Inclined Length of Prism given Saturated Unit Weight

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

Go Vertical Stress on Prism given Saturated Unit Weight

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

Go Normal Stress Component given Saturated Unit Weight

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

See More

How to Evaluate Shear Stress given Submerged Unit Weight?

Shear Stress given Submerged Unit Weight evaluator uses Shear Stress in Soil Mechanics = Shear Strength in KN per Cubic Meter/((Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil)))) to evaluate the Shear Stress in Soil Mechanics, The Shear Stress given Submerged Unit Weight is defined as the value of shear stress when we have prior information of other parameters used. Shear Stress in Soil Mechanics is denoted by ζ_soil symbol.

How to evaluate Shear Stress given Submerged Unit Weight using this online evaluator? To use this online evaluator for Shear Stress given Submerged Unit Weight, enter Shear Strength in KN per Cubic Meter (τ_f), Submerged Unit Weight in KN per Cubic Meter (y_S), Angle of Internal Friction (φ), Saturated Unit Weight of Soil (γ_saturated) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Shear Stress given Submerged Unit Weight

What is the formula to find Shear Stress given Submerged Unit Weight?

The formula of Shear Stress given Submerged Unit Weight is expressed as Shear Stress in Soil Mechanics = Shear Strength in KN per Cubic Meter/((Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil)))). Here is an example- 0.023165 = 4920/((5000*tan((0.802851455917241)))/(11890*tan((1.11701072127616)))).

How to calculate Shear Stress given Submerged Unit Weight?

With Shear Strength in KN per Cubic Meter (τ_f), Submerged Unit Weight in KN per Cubic Meter (y_S), Angle of Internal Friction (φ), Saturated Unit Weight of Soil (γ_saturated) & Angle of Inclination to Horizontal in Soil (i) we can find Shear Stress given Submerged Unit Weight using the formula - Shear Stress in Soil Mechanics = Shear Strength in KN per Cubic Meter/((Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil)))). This formula also uses Tangent (tan) function(s).

What are the other ways to Calculate Shear Stress in Soil Mechanics?

Here are the different ways to Calculate Shear Stress in Soil Mechanics-

Shear Stress in Soil Mechanics=(Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))

Can the Shear Stress given Submerged Unit Weight be negative?

No, the Shear Stress given Submerged Unit Weight, measured in Stress cannot be negative.

Which unit is used to measure Shear Stress given Submerged Unit Weight?

Shear Stress given Submerged Unit Weight is usually measured using the Kilonewton per Square Meter[kN/m²] for Stress. Pascal[kN/m²], Newton per Square Meter[kN/m²], Newton per Square Millimeter[kN/m²] are the few other units in which Shear Stress given Submerged Unit Weight can be measured.

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