Vertical Stress at Point in Boussinesq Equation Calculator

✖Total Concentrated Surface Load in Boussinesq Eq. is the load applied to a specific, localized area on the surface of the ground.ⓘ Total Concentrated Surface Load in Boussinesq Eq. [P]			+10% -10%
✖Depth of Point is the vertical distance from the ground surface to a specific point of interest below the surface.ⓘ Depth of Point [z]			+10% -10%
✖Horizontal Distance is the straight-line distance measured horizontally between two points.ⓘ Horizontal Distance [r]			+10% -10%

✖Vertical Stress at Point in Boussinesq Equation is the stress acting perpendicular to the surface.ⓘ Vertical Stress at Point in Boussinesq Equation [σ_z]

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Vertical Stress at Point in Boussinesq Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vertical Stress at Point in Boussinesq Equation = ((3*Total Concentrated Surface Load in Boussinesq Eq.)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2))
σ_z = ((3*P)/(2*pi*(z)^2))*((1+(r/z)^2)^(5/2))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Vertical Stress at Point in Boussinesq Equation - (Measured in Pascal) - Vertical Stress at Point in Boussinesq Equation is the stress acting perpendicular to the surface.
Total Concentrated Surface Load in Boussinesq Eq. - (Measured in Newton) - Total Concentrated Surface Load in Boussinesq Eq. is the load applied to a specific, localized area on the surface of the ground.
Depth of Point - (Measured in Meter) - Depth of Point is the vertical distance from the ground surface to a specific point of interest below the surface.
Horizontal Distance - (Measured in Meter) - Horizontal Distance is the straight-line distance measured horizontally between two points.

STEP 1: Convert Input(s) to Base Unit

Total Concentrated Surface Load in Boussinesq Eq.: 19.87 Newton --> 19.87 Newton No Conversion Required
Depth of Point: 15 Meter --> 15 Meter No Conversion Required
Horizontal Distance: 25 Meter --> 25 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_z = ((3*P)/(2*pi*(z)^2))*((1+(r/z)^2)^(5/2)) --> ((3*19.87)/(2*pi*(15)^2))*((1+(25/15)^2)^(5/2))

Evaluating ... ...

σ_z = 1.16962799448242

STEP 3: Convert Result to Output's Unit

1.16962799448242 Pascal --> No Conversion Required

FINAL ANSWER

1.16962799448242 ≈ 1.169628 Pascal <-- Vertical Stress at Point in Boussinesq Equation

(Calculation completed in 00.004 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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< Vertical Pressure in Soils Calculators

Vertical Stress at Point in Boussinesq Equation

LaTeX Go Vertical Stress at Point in Boussinesq Equation = ((3*Total Concentrated Surface Load in Boussinesq Eq.)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2))

Vertical Stress at Point in Westergaard Equation

LaTeX Go Vertical Stress at Point in Westergaard Equation = ((Total Concentrated Surface Load in Boussinesq Eq./(pi*(Depth of Point)^2))*(1+2*(Horizontal Distance/Depth of Point)^2)^(3/2))

Total Concentrated Surface Load in Boussinesq Equation

LaTeX Go Total Concentrated Surface Load in Boussinesq Eq. = (2*pi*Vertical Stress at Point in Boussinesq Equation*(Depth of Point)^2)/(3*(1+(Horizontal Distance/Depth of Point)^2)^(5/2))

Total Concentrated Surface Load in Westergaard Equation

LaTeX Go Total Concentrated Surface Load in Westergaard Eq. = (Vertical Stress at Point in Boussinesq Equation*pi*(Depth of Point)^2)/((1+2*(Horizontal Distance/Depth of Point)^2)^(3/2))

Vertical Stress at Point in Boussinesq Equation Formula

LaTeX Go

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 at Point in Boussinesq Equation?

Vertical Stress at Point in Boussinesq Equation calculator uses Vertical Stress at Point in Boussinesq Equation = ((3*Total Concentrated Surface Load in Boussinesq Eq.)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2)) to calculate the Vertical Stress at Point in Boussinesq Equation, The Vertical Stress at Point in Boussinesq Equation formula is defined as vertical pressure acting on the ground. Vertical Stress at Point in Boussinesq Equation is denoted by σ_z symbol.

How to calculate Vertical Stress at Point in Boussinesq Equation using this online calculator? To use this online calculator for Vertical Stress at Point in Boussinesq Equation, enter Total Concentrated Surface Load in Boussinesq Eq. (P), Depth of Point (z) & Horizontal Distance (r) and hit the calculate button. Here is how the Vertical Stress at Point in Boussinesq Equation calculation can be explained with given input values -> 1.17728 = ((3*19.87)/(2*pi*(15)^2))*((1+(25/15)^2)^(5/2)).

FAQ

What is Vertical Stress at Point in Boussinesq Equation?

The Vertical Stress at Point in Boussinesq Equation formula is defined as vertical pressure acting on the ground and is represented as σ_z = ((3*P)/(2*pi*(z)^2))*((1+(r/z)^2)^(5/2)) or Vertical Stress at Point in Boussinesq Equation = ((3*Total Concentrated Surface Load in Boussinesq Eq.)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2)). Total Concentrated Surface Load in Boussinesq Eq. is the load applied to a specific, localized area on the surface of the ground, Depth of Point is the vertical distance from the ground surface to a specific point of interest below the surface & Horizontal Distance is the straight-line distance measured horizontally between two points.

How to calculate Vertical Stress at Point in Boussinesq Equation?

The Vertical Stress at Point in Boussinesq Equation formula is defined as vertical pressure acting on the ground is calculated using Vertical Stress at Point in Boussinesq Equation = ((3*Total Concentrated Surface Load in Boussinesq Eq.)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2)). To calculate Vertical Stress at Point in Boussinesq Equation, you need Total Concentrated Surface Load in Boussinesq Eq. (P), Depth of Point (z) & Horizontal Distance (r). With our tool, you need to enter the respective value for Total Concentrated Surface Load in Boussinesq Eq, Depth of Point & Horizontal Distance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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