Depth of Prism given Normal Stress and Saturated Unit Weight Calculator

✖Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress in Soil Mechanics [σ_n]			+10% -10%
✖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%
✖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%

✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism given Normal Stress and Saturated Unit Weight [z]

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Depth of Prism given Normal Stress and Saturated Unit Weight Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Prism = Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
z = σ_n/(γ_saturated*(cos((i*pi)/180))^2)
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Normal Stress in Soil Mechanics - (Measured in Pascal) - Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force.
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.
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

Normal Stress in Soil Mechanics: 77.36 Kilonewton per Square Meter --> 77360 Pascal (Check conversion here)
Saturated Unit Weight of Soil: 11.89 Kilonewton per Cubic Meter --> 11890 Newton per Cubic Meter (Check conversion here)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = σ_n/(γ_saturated*(cos((i*pi)/180))^2) --> 77360/(11890*(cos((1.11701072127616*pi)/180))^2)

Evaluating ... ...

z = 6.50878133401738

STEP 3: Convert Result to Output's Unit

6.50878133401738 Meter --> No Conversion Required

FINAL ANSWER

6.50878133401738 ≈ 6.508781 Meter <-- Depth of Prism

(Calculation completed in 00.021 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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Depth of Prism given Saturated Unit Weight

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

Saturated Unit Weight given Weight of Soil Prism

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

Saturated Unit Weight given Vertical Stress on Prism

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

Angle of Inclination given Saturated Unit Weight

LaTeX Go Angle of Inclination to Horizontal in Soil = acos(Weight of Prism in Soil Mechanics/(Unit Weight of Soil*Depth of Prism*Inclined Length of Prism))

Depth of Prism given Normal Stress and Saturated Unit Weight Formula

LaTeX Go

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

What is Normal Stress?

A normal stress is a stress that occurs when a member is loaded by an axial force. The value of the normal force for any prismatic section is simply the force divided by the cross sectional area.

How to Calculate Depth of Prism given Normal Stress and Saturated Unit Weight?

Depth of Prism given Normal Stress and Saturated Unit Weight calculator uses Depth of Prism = Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to calculate the Depth of Prism, The Depth of Prism given Normal Stress and Saturated Unit Weight calculates the value of depth of prism when we have prior information of other parameters used. Depth of Prism is denoted by z symbol.

How to calculate Depth of Prism given Normal Stress and Saturated Unit Weight using this online calculator? To use this online calculator for Depth of Prism given Normal Stress and Saturated Unit Weight, enter Normal Stress in Soil Mechanics (σ_n), Saturated Unit Weight of Soil (γ_saturated) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Depth of Prism given Normal Stress and Saturated Unit Weight calculation can be explained with given input values -> 3.143331 = 77360/(11890*(cos((1.11701072127616*pi)/180))^2).

FAQ

What is Depth of Prism given Normal Stress and Saturated Unit Weight?

The Depth of Prism given Normal Stress and Saturated Unit Weight calculates the value of depth of prism when we have prior information of other parameters used and is represented as z = σ_n/(γ_saturated*(cos((i*pi)/180))^2) or Depth of Prism = Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force, Saturated Unit Weight of Soil is the ratio of mass of saturated soil sample to total volume & 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 Depth of Prism given Normal Stress and Saturated Unit Weight?

The Depth of Prism given Normal Stress and Saturated Unit Weight calculates the value of depth of prism when we have prior information of other parameters used is calculated using Depth of Prism = Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). To calculate Depth of Prism given Normal Stress and Saturated Unit Weight, you need Normal Stress in Soil Mechanics (σ_n), Saturated Unit Weight of Soil (γ_saturated) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Normal Stress in Soil Mechanics, Saturated Unit Weight of Soil & 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 Depth of Prism?

In this formula, Depth of Prism uses Normal Stress in Soil Mechanics, Saturated Unit Weight of Soil & Angle of Inclination to Horizontal in Soil. We can use 3 other way(s) to calculate the same, which is/are as follows -

Depth of Prism = Weight of Prism in Soil Mechanics/(Saturated Unit Weight in Newton per Cubic Meter*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism = Vertical Stress at a Point in Kilopascal/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism = Shear Stress in Soil Mechanics/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))

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