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Shear Strength given Submerged Unit Weight Formula

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

τ f = \frac{ζ soil \cdot y S \cdot \tan (\frac{φ \cdot π}{180})}{γ saturated \cdot \tan (\frac{i \cdot π}{180})}

τ_f - Shear Strength in KN per Cubic Meter?ζ_soil - Shear Stress in Soil Mechanics?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?π - Archimedes' constant?

Shear Strength given Submerged Unit Weight Example

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

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

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

0.2146 = \frac{0.71 \cdot 5 \cdot \tan (\frac{46 \cdot 3.1416}{180})}{11.89 \cdot \tan (\frac{64 \cdot 3.1416}{180})}

0.2146kN/m² = \frac{0.71kN/m² \cdot 5kN/m³ \cdot \tan (\frac{46° \cdot 3.1416}{180})}{11.89kN/m³ \cdot \tan (\frac{64° \cdot 3.1416}{180})}

0.2146 = \frac{0.71 \cdot 5 \cdot \tan (\frac{46 \cdot 3.1416}{180})}{11.89 \cdot \tan (\frac{64 \cdot 3.1416}{180})}

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Shear Strength given Submerged Unit Weight Solution

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

FIRST Step Consider the formula

τ f = \frac{ζ soil \cdot y S \cdot \tan (\frac{φ \cdot π}{180})}{γ saturated \cdot \tan (\frac{i \cdot π}{180})}

Next Step Substitute values of Variables

∴

τ f = \frac{0.71kN/m² \cdot 5kN/m³ \cdot \tan (\frac{46° \cdot π}{180})}{11.89kN/m³ \cdot \tan (\frac{64° \cdot π}{180})}

Next Step Substitute values of Constants

∴

τ f = \frac{0.71kN/m² \cdot 5kN/m³ \cdot \tan (\frac{46° \cdot 3.1416}{180})}{11.89kN/m³ \cdot \tan (\frac{64° \cdot 3.1416}{180})}

Next Step Convert Units

∴

τ f = \frac{710Pa \cdot 5000N/m³ \cdot \tan (\frac{0.8029rad \cdot 3.1416}{180})}{11890N/m³ \cdot \tan (\frac{1.117rad \cdot 3.1416}{180})}

Next Step Prepare to Evaluate

∴

τ f = \frac{710 \cdot 5000 \cdot \tan (\frac{0.8029 \cdot 3.1416}{180})}{11890 \cdot \tan (\frac{1.117 \cdot 3.1416}{180})}

Next Step Evaluate

∴

τ f = 214.584206856326Pa

Next Step Convert to Output's Unit

∴

τ f = 0.214584206856326kN/m²

LAST Step Rounding Answer

∴

τ f = 0.2146kN/m²

Shear Strength given Submerged Unit Weight Formula Elements

Variables

Constants

Functions

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.

Formulas to find Shear Strength in KN per Cubic Meter

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

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.

Formulas to find Submerged Unit Weight in KN per Cubic Meter

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.

Formulas to find Angle of Internal Friction

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

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)

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})

How to Evaluate Shear Strength given Submerged Unit Weight?

Shear Strength given Submerged Unit Weight evaluator uses Shear Strength in KN per Cubic Meter = (Shear Stress in Soil Mechanics*Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)) to evaluate the Shear Strength in KN per Cubic Meter, The Shear Strength given Submerged Unit Weight is defined as the value of shear strength of soil when we have prior information of other parameters used. Shear Strength in KN per Cubic Meter is denoted by τ_f symbol.

How to evaluate Shear Strength given Submerged Unit Weight using this online evaluator? To use this online evaluator for Shear Strength given Submerged Unit Weight, enter Shear Stress in Soil Mechanics (ζ_soil), 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 Strength given Submerged Unit Weight

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

The formula of Shear Strength given Submerged Unit Weight is expressed as Shear Strength in KN per Cubic Meter = (Shear Stress in Soil Mechanics*Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)). Here is an example- 0.000215 = (710*5000*tan((0.802851455917241*pi)/180))/(11890*tan((1.11701072127616*pi)/180)).

How to calculate Shear Strength given Submerged Unit Weight?

With Shear Stress in Soil Mechanics (ζ_soil), 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 Strength given Submerged Unit Weight using the formula - Shear Strength in KN per Cubic Meter = (Shear Stress in Soil Mechanics*Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)). This formula also uses Archimedes' constant and Tangent (tan) function(s).

Can the Shear Strength given Submerged Unit Weight be negative?

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

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

Shear Strength 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 Strength given Submerged Unit Weight can be measured.

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Shear Strength given Submerged Unit Weight Formula

Shear Strength given Submerged Unit Weight Example

Shear Strength given Submerged Unit Weight Solution

Shear Strength given Submerged Unit Weight Formula Elements

Other formulas in Steady State Seepage Analysis Along The Slopes category

How to Evaluate Shear Strength given Submerged Unit Weight?

FAQs on Shear Strength given Submerged Unit Weight

Variable Name