Shear Stress Component given Saturated Unit Weight Calculator

✖Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.ⓘ Saturated Unit Weight of Soil [γ_saturated]			+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 in Soil Mechanics is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress Component given Saturated Unit Weight [ζ_soil]

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Formula

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Shear Stress Component given Saturated Unit Weight

Formula

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

Example

0.695229 kN/m² = (11.89 kN/m³ \cdot 3 m \cdot \cos (\frac{64 ° \cdot π}{180}) \cdot \sin (\frac{64 ° \cdot π}{180}))

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Shear Stress Component given Saturated Unit Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
ζ_soil = (γ_saturated*z*cos((i*pi)/180)*sin((i*pi)/180))
This formula uses 1 Constants, 2 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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 in Soil Mechanics - (Measured in Pascal) - 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.
Saturated Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume.
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

Saturated Unit Weight of Soil: 11.89 Kilonewton per Cubic Meter --> 11890 Newton per Cubic Meter (Check conversion here)
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

ζ_soil = (γ_saturated*z*cos((i*pi)/180)*sin((i*pi)/180)) --> (11890*3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180))

Evaluating ... ...

ζ_soil = 695.228824589117

STEP 3: Convert Result to Output's Unit

695.228824589117 Pascal -->0.695228824589118 Kilonewton per Square Meter (Check conversion here)

FINAL ANSWER

0.695228824589118 ≈ 0.695229 Kilonewton per Square Meter <-- Shear Stress in Soil Mechanics

(Calculation completed in 00.021 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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< Steady State Seepage Analysis Along The Slopes Calculators

Inclined Length of Prism given Saturated Unit Weight

Go Inclined Length of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Weight of Soil Prism given Saturated Unit Weight

Go Weight of Prism in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Vertical Stress on Prism given Saturated Unit Weight

Go Vertical Stress at a Point in Kilopascal = (Saturated Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Normal Stress Component given Saturated Unit Weight

Go Normal Stress in Soil Mechanics = (Saturated Unit Weight of Soil*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Shear Stress Component given Saturated 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 Saturated Unit Weight?

Shear Stress Component given Saturated Unit Weight calculator uses 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)) to calculate the Shear Stress in Soil Mechanics, The Shear Stress Component given Saturated 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 calculate Shear Stress Component given Saturated Unit Weight using this online calculator? To use this online calculator for Shear Stress Component given Saturated Unit Weight, enter Saturated Unit Weight of Soil (γ_saturated), 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 Saturated Unit Weight calculation can be explained with given input values -> 0.000695 = (11890*3*cos((1.11701072127616*pi)/180)*sin((1.11701072127616*pi)/180)).

FAQ

What is Shear Stress Component given Saturated Unit Weight?

The Shear Stress Component given Saturated Unit Weight is defined as the value of shear stress when we have prior information of other parameters used and is represented as ζ_soil = (γ_saturated*z*cos((i*pi)/180)*sin((i*pi)/180)) or 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)). Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume, 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 Saturated Unit Weight?

The Shear Stress Component given Saturated Unit Weight is defined as the value of shear stress when we have prior information of other parameters used is calculated using 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)). To calculate Shear Stress Component given Saturated Unit Weight, you need Saturated Unit Weight of Soil (γ_saturated), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Saturated Unit Weight of Soil, 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 Shear Stress in Soil Mechanics?

In this formula, Shear Stress in Soil Mechanics uses Saturated Unit Weight of Soil, Depth of Prism & Angle of Inclination to Horizontal in Soil. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))))

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