Vertical Stress at Point in Boussinesq Equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Vertical Stress at Point = ((3*Total Concentrated Surface Load)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2))
σz = ((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 - (Measured in Pascal) - Vertical Stress at Point is the stress acting perpendicular to the surface.
Total Concentrated Surface Load - (Measured in Newton) - Total Concentrated Surface Load is the value of force applied on the surface.
Depth of Point - (Measured in Meter) - Depth of Point at which stress acts, measured vertically downward from surface.
Horizontal Distance - (Measured in Meter) - Horizontal Distance from projection of surface load P to point at which stress is acting.
STEP 1: Convert Input(s) to Base Unit
Total Concentrated Surface Load: 20 Newton --> 20 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
σz = ((3*P)/(2*pi*(z)^2))*((1+(r/z)^2)^(5/2)) --> ((3*20)/(2*pi*(15)^2))*((1+(25/15)^2)^(5/2))
Evaluating ... ...
σz = 1.17728031653993
STEP 3: Convert Result to Output's Unit
1.17728031653993 Pascal --> No Conversion Required
FINAL ANSWER
1.17728031653993 1.17728 Pascal <-- Vertical Stress at Point
(Calculation completed in 00.004 seconds)

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!

4 Vertical Pressure in Soils Calculators

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

Vertical Stress at Point in Boussinesq Equation Formula

Vertical Stress at Point = ((3*Total Concentrated Surface Load)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2))
σz = ((3*P)/(2*pi*(z)^2))*((1+(r/z)^2)^(5/2))

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 = ((3*Total Concentrated Surface Load)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2)) to calculate the Vertical Stress at Point, The Vertical Stress at Point in Boussinesq Equation formula is defined as vertical pressure acting on the ground. Vertical Stress at Point is denoted by σz 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 (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 -> 740266.4 = ((3*20)/(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 σz = ((3*P)/(2*pi*(z)^2))*((1+(r/z)^2)^(5/2)) or Vertical Stress at Point = ((3*Total Concentrated Surface Load)/(2*pi*(Depth of Point)^2))*((1+(Horizontal Distance/Depth of Point)^2)^(5/2)). Total Concentrated Surface Load is the value of force applied on the surface, Depth of Point at which stress acts, measured vertically downward from surface & Horizontal Distance from projection of surface load P to point at which stress is acting.
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 = ((3*Total Concentrated Surface Load)/(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 (P), Depth of Point (z) & Horizontal Distance (r). With our tool, you need to enter the respective value for Total Concentrated Surface Load, 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.
How many ways are there to calculate Vertical Stress at Point?
In this formula, Vertical Stress at Point uses Total Concentrated Surface Load, Depth of Point & Horizontal Distance. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Vertical Stress at Point = ((Total Concentrated Surface Load/(pi*(Depth of Point)^2))*(1+2*(Horizontal Distance/Depth of Point)^2)^(3/2))
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!