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Shear Stress Component given Unit Weight of Soil Formula

GoShear Stress Component given Vertical Stress Formula

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Ultimate 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 = (γ \cdot z \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180}))

ζ - Ultimate Shear Stress in Soil Mechanics?γ - Unit Weight of Soil?z - Depth of Prism?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Shear Stress Component given Unit Weight of Soil Example

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Here is how the Shear Stress Component given Unit Weight of Soil equation looks like with Values.

Here is how the Shear Stress Component given Unit Weight of Soil equation looks like with Units.

Here is how the Shear Stress Component given Unit Weight of Soil equation looks like.

1.0525 = (18 \cdot 3 \cdot \cos (\frac{64 \cdot 3.1416}{180}) \cdot \sin (\frac{64 \cdot 3.1416}{180}))

1.0525kN/m² = (18kN/m³ \cdot 3m \cdot \cos (\frac{64° \cdot 3.1416}{180}) \cdot \sin (\frac{64° \cdot 3.1416}{180}))

1.0525 = (18 \cdot 3 \cdot \cos (\frac{64 \cdot 3.1416}{180}) \cdot \sin (\frac{64 \cdot 3.1416}{180}))

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Shear Stress Component given Unit Weight of Soil Solution

Follow our step by step solution on how to calculate Shear Stress Component given Unit Weight of Soil?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ζ = (18kN/m³ \cdot 3m \cdot \cos (\frac{64° \cdot π}{180}) \cdot \sin (\frac{64° \cdot π}{180}))

Next Step Substitute values of Constants

∴

ζ = (18kN/m³ \cdot 3m \cdot \cos (\frac{64° \cdot 3.1416}{180}) \cdot \sin (\frac{64° \cdot 3.1416}{180}))

Next Step Convert Units

∴

ζ = (18000N/m³ \cdot 3m \cdot \cos (\frac{1.117rad \cdot 3.1416}{180}) \cdot \sin (\frac{1.117rad \cdot 3.1416}{180}))

Next Step Prepare to Evaluate

∴

ζ = (18000 \cdot 3 \cdot \cos (\frac{1.117 \cdot 3.1416}{180}) \cdot \sin (\frac{1.117 \cdot 3.1416}{180}))

Next Step Evaluate

∴

ζ = 1052.49107170766Pa

Next Step Convert to Output's Unit

∴

ζ = 1.05249107170766kN/m²

LAST Step Rounding Answer

∴

ζ = 1.0525kN/m²

Shear Stress Component given Unit Weight of Soil Formula Elements

Variables

Constants

Functions

Ultimate Shear Stress in Soil Mechanics

Ultimate 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

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Ultimate Shear Stress in Soil Mechanics

Unit Weight of Soil

Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.

Symbol: γ

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Unit Weight of Soil

Depth of Prism

Depth of Prism is the length of prism along z direction.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Prism

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

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Ultimate Shear Stress in Soil Mechanics

Go Shear Stress Component given Vertical Stress

ζ = σ zkp \cdot \sin (\frac{i \cdot π}{180})

Other formulas in Shear Stress Component category

Go Angle of Inclination given Shear Stress Component

i = a \sin (\frac{τ u}{σ z})

Go Shear Strength of Soil given Factor of Safety

τ f = ζ \cdot f s

Go Settlement of Rectangular Spreader Mat

S mat = S plate \cdot {(B mat \cdot \frac{L mat}{{(D plate)}^{2}})}^{0.5}

How to Evaluate Shear Stress Component given Unit Weight of Soil?

Shear Stress Component given Unit Weight of Soil evaluator uses Ultimate Shear Stress in Soil Mechanics = (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)) to evaluate the Ultimate Shear Stress in Soil Mechanics, The Shear Stress Component given Unit Weight of Soil is defined as the value of shear stress when we have prior information of other parameters used. Ultimate Shear Stress in Soil Mechanics is denoted by ζ symbol.

How to evaluate Shear Stress Component given Unit Weight of Soil using this online evaluator? To use this online evaluator for Shear Stress Component given Unit Weight of Soil, enter Unit Weight of Soil (γ), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Shear Stress Component given Unit Weight of Soil

What is the formula to find Shear Stress Component given Unit Weight of Soil?

The formula of Shear Stress Component given Unit Weight of Soil is expressed as Ultimate Shear Stress in Soil Mechanics = (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)). Here is an example- 0.001052 = (18000*3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180)).

How to calculate Shear Stress Component given Unit Weight of Soil?

With Unit Weight of Soil (γ), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) we can find Shear Stress Component given Unit Weight of Soil using the formula - Ultimate Shear Stress in Soil Mechanics = (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)). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

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

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

Ultimate Shear Stress in Soil Mechanics=Vertical Stress at a Point in Kilopascal*sin((Angle of Inclination to Horizontal in Soil*pi)/180)

Can the Shear Stress Component given Unit Weight of Soil be negative?

No, the Shear Stress Component given Unit Weight of Soil, measured in Pressure cannot be negative.

Which unit is used to measure Shear Stress Component given Unit Weight of Soil?

Shear Stress Component given Unit Weight of Soil is usually measured using the Kilonewton per Square Meter[kN/m²] for Pressure. Pascal[kN/m²], Kilopascal[kN/m²], Bar[kN/m²] are the few other units in which Shear Stress Component given Unit Weight of Soil can be measured.

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Shear Stress Component given Unit Weight of Soil Formula

​GoShear Stress Component given Vertical Stress Formula

Shear Stress Component given Unit Weight of Soil Example

Shear Stress Component given Unit Weight of Soil Solution

Shear Stress Component given Unit Weight of Soil Formula Elements

Other Formulas to find Ultimate Shear Stress in Soil Mechanics

Other formulas in Shear Stress Component category

How to Evaluate Shear Stress Component given Unit Weight of Soil?

FAQs on Shear Stress Component given Unit Weight of Soil

Variable Name

GoShear Stress Component given Vertical Stress Formula