Vertical Stress on Surface of Prism given Unit Weight of Soil Calculator

✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism [z]			+10% -10%
✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [γ]			+10% -10%
✖Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination [I]			+10% -10%

✖Vertical Stress at a Point is the stress acting perpendicular to the surface.ⓘ Vertical Stress on Surface of Prism given Unit Weight of Soil [σ_z]

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Formula

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Vertical Stress on Surface of Prism given Unit Weight of Soil

Formula

`"σ"_{"z"} = ("z"*"γ"*cos(("I")))`

Example

`"9.377002MPa"=("3m"*"18kN/m³"*cos(("80°")))`

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Download Stability Analysis of Infinite Slopes in Prism Formulas PDF

Vertical Stress on Surface of Prism given Unit Weight of Soil Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination)))
σ_z = (z*γ*cos((I)))
This formula uses 1 Functions, 4 Variables

Functions Used

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

Vertical Stress at a Point - (Measured in Megapascal) - Vertical Stress at a Point is the stress acting perpendicular to the surface.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Unit Weight of Soil - (Measured in Kilonewton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Angle of Inclination - (Measured in Radian) - Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.

STEP 1: Convert Input(s) to Base Unit

Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18 Kilonewton per Cubic Meter No Conversion Required
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_z = (z*γ*cos((I))) --> (3*18*cos((1.3962634015952)))

Evaluating ... ...

σ_z = 9.37700159402826

STEP 3: Convert Result to Output's Unit

9377001.59402826 Pascal -->9.37700159402826 Megapascal (Check conversion here)

FINAL ANSWER

9.37700159402826 ≈ 9.377002 Megapascal <-- Vertical Stress at a Point

(Calculation completed in 00.004 seconds)

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Credits

Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2200+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 23 Stability Analysis of Infinite Slopes in Prism Calculators

Unit Weight of Soil given Factor of Safety for Cohesive Soil

Go Unit Weight of Soil = Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))

Cohesion given Factor of Safety for Cohesive Soil

Go Cohesion of Soil = (Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))

Depth of Prism given Factor of Safety for Cohesive Soil

Go Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination)))

Factor of Safety for Cohesive Soil given Cohesion

Go Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))

Inclined Length along Slope given Weight of Soil Prism

Go Inclined Length = Weight of Prism/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination)))

Unit Weight of Soil given Weight of Soil Prism

Go Unit Weight of Soil = Weight of Prism/(Depth of Prism*Inclined Length*cos((Angle of Inclination)))

Weight of Soil Prism in Stability Analysis

Go Weight of Prism = (Unit Weight of Soil*Depth of Prism*Inclined Length*cos((Angle of Inclination)))

Depth of Prism given Weight of Soil Prism

Go Depth of Prism = Weight of Prism/(Unit Weight of Soil*Inclined Length*cos((Angle of Inclination)))

Angle of Inclination given Weight of Soil Prism

Go Angle of Inclination = acos(Weight of Prism/(Unit Weight of Soil*Depth of Prism*Inclined Length))

Unit Weight of Soil given Vertical Stress on Surface of Prism

Go Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))

Depth of Prism given Vertical Stress on Surface of Prism

Go Depth of Prism = Vertical Stress at a Point in Pascal/(Unit Weight of Soil*cos((Angle of Inclination)))

Angle of Inclination given Vertical Stress on Surface of Prism

Go Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil))

Inclined Length along Slope given Volume Per Unit Length of Prism

Go Inclined Length = Volume per unit length of prism/(Depth of Prism*cos((Angle of Inclination)))

Depth of Prism given Volume per Unit Length of Prism

Go Depth of Prism = Volume per unit length of prism/(Inclined Length*cos((Angle of Inclination)))

Volume Per Unit Length of Prism

Go Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination)))

Vertical Stress on Surface of Prism given Unit Weight of Soil

Go Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination)))

Angle of Inclination given Volume per Unit Length of Prism

Go Angle of Inclination = acos(Volume per unit length of prism/(Depth of Prism*Inclined Length))

Inclined Length along Slope given Horizontal Length of Prism

Go Inclined Length = Horizontal Length of Prism/cos((Angle of Inclination))

Horizontal Length of Prism

Go Horizontal Length of Prism = Inclined Length*cos((Angle of Inclination))

Angle of Inclination given Horizontal Length of Prism

Go Angle of Inclination = acos(Horizontal Length of Prism/Inclined Length)

Weight of Soil Prism given Vertical Stress on Surface of Prism

Go Weight of Prism = Vertical Stress at a Point in Pascal*Inclined Length

Inclined Length along Slope given Vertical Stress on Surface of Prism

Go Inclined Length = Weight of Prism/Vertical Stress at a Point*5

Vertical Stress on Surface of Prism

Go Vertical Stress at a Point = Weight of Prism/Inclined Length

Vertical Stress on Surface of Prism given Unit Weight of Soil Formula

Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination)))
σ_z = (z*γ*cos((I)))

What is Vertical Stress?

In other words the vertical stress (σv) and horizontal stress (σH) are principal stresses. The vertical stress on element A can be determined simply from the mass of the. overlying material.

How to Calculate Vertical Stress on Surface of Prism given Unit Weight of Soil?

Vertical Stress on Surface of Prism given Unit Weight of Soil calculator uses Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination))) to calculate the Vertical Stress at a Point, The Vertical Stress on Surface of Prism given Unit Weight of Soil is defined as the product of unit weight of soil and depth below the surface. Vertical Stress at a Point is denoted by σ_z symbol.

How to calculate Vertical Stress on Surface of Prism given Unit Weight of Soil using this online calculator? To use this online calculator for Vertical Stress on Surface of Prism given Unit Weight of Soil, enter Depth of Prism (z), Unit Weight of Soil (γ) & Angle of Inclination (I) and hit the calculate button. Here is how the Vertical Stress on Surface of Prism given Unit Weight of Soil calculation can be explained with given input values -> 9.4E-9 = (3*18000*cos((1.3962634015952))).

FAQ

What is Vertical Stress on Surface of Prism given Unit Weight of Soil?

The Vertical Stress on Surface of Prism given Unit Weight of Soil is defined as the product of unit weight of soil and depth below the surface and is represented as σ_z = (z*γ*cos((I))) or Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination))). Depth of Prism is the length of prism along z direction, Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil & Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.

How to calculate Vertical Stress on Surface of Prism given Unit Weight of Soil?

The Vertical Stress on Surface of Prism given Unit Weight of Soil is defined as the product of unit weight of soil and depth below the surface is calculated using Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination))). To calculate Vertical Stress on Surface of Prism given Unit Weight of Soil, you need Depth of Prism (z), Unit Weight of Soil (γ) & Angle of Inclination (I). With our tool, you need to enter the respective value for Depth of Prism, Unit Weight of Soil & Angle of Inclination 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 Vertical Stress at a Point?

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

Vertical Stress at a Point = Weight of Prism/Inclined Length

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