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Total Concentrated Surface Load in Westergaard Equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
total_concentrated_surface_load = (Vertical stress at a point*pi*(Depth of point)^2)/((1+2*(Horizontal distance/Depth of point)^2)^(3/2))
P = (σz*pi*(z)^2)/((1+2*(r/z)^2)^(3/2))
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Vertical stress at a point - Vertical stress at a point is the stress acting perpendicular to the surface. (Measured in Megapascal)
Depth of point - Depth of point at which stress acts, measured vertically downward from surface. (Measured in Meter)
Horizontal distance - Horizontal distance from projection of surface load P to point at which stress is acting. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Vertical stress at a point: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Depth of point: 2 Meter --> 2 Meter No Conversion Required
Horizontal distance: 5 Meter --> 5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = (σz*pi*(z)^2)/((1+2*(r/z)^2)^(3/2)) --> (10000000*pi*(2)^2)/((1+2*(5/2)^2)^(3/2))
Evaluating ... ...
P = 2533431.76328269
STEP 3: Convert Result to Output's Unit
2533431.76328269 Newton --> No Conversion Required
FINAL ANSWER
2533431.76328269 Newton <-- Total concentrated surface load
(Calculation completed in 00.015 seconds)

4 Vertical Pressures in Soils Calculators

Vertical Stress at a Point in Boussinesq Equation
vertical_stress_at_a_point = ((3*Total concentrated surface load)/(2*pi*(Depth of point)^2))*((1+(Horizontal distance/Depth of point)^2)^(5/2)) Go
Total Concentrated Surface Load in Boussinesq Equation
total_concentrated_surface_load = (2*pi*Vertical stress at a point*(Depth of point)^2)/(3*(1+(Horizontal distance/Depth of point)^2)^(5/2)) Go
Vertical Stress at a Point in Westergaard Equation
vertical_stress_at_a_point = ((Total concentrated surface load/(pi*(Depth of point)^2))*(1+2*(Horizontal distance/Depth of point)^2)^(3/2)) Go
Total Concentrated Surface Load in Westergaard Equation
total_concentrated_surface_load = (Vertical stress at a point*pi*(Depth of point)^2)/((1+2*(Horizontal distance/Depth of point)^2)^(3/2)) Go

Total Concentrated Surface Load in Westergaard Equation Formula

total_concentrated_surface_load = (Vertical stress at a point*pi*(Depth of point)^2)/((1+2*(Horizontal distance/Depth of point)^2)^(3/2))
P = (σz*pi*(z)^2)/((1+2*(r/z)^2)^(3/2))

What is concentrated surface load ?

A force that is negligible because of a small contact area; a beam supported on a soil represents a concentrated load on the soil. A load that is applied to a relatively small area compared with the size of the loaded member.

How to Calculate Total Concentrated Surface Load in Westergaard Equation?

Total Concentrated Surface Load in Westergaard Equation calculator uses total_concentrated_surface_load = (Vertical stress at a point*pi*(Depth of point)^2)/((1+2*(Horizontal distance/Depth of point)^2)^(3/2)) to calculate the Total concentrated surface load, The Total Concentrated Surface Load in Westergaard Equation formula is defined as the total force acting on the soil surface. Total concentrated surface load and is denoted by P symbol.

How to calculate Total Concentrated Surface Load in Westergaard Equation using this online calculator? To use this online calculator for Total Concentrated Surface Load in Westergaard Equation, enter Vertical stress at a point z), Depth of point (z) and Horizontal distance (r) and hit the calculate button. Here is how the Total Concentrated Surface Load in Westergaard Equation calculation can be explained with given input values -> 2533.432 = (10000*pi*(2)^2)/((1+2*(5/2)^2)^(3/2)).

FAQ

What is Total Concentrated Surface Load in Westergaard Equation?
The Total Concentrated Surface Load in Westergaard Equation formula is defined as the total force acting on the soil surface and is represented as P = (σz*pi*(z)^2)/((1+2*(r/z)^2)^(3/2)) or total_concentrated_surface_load = (Vertical stress at a point*pi*(Depth of point)^2)/((1+2*(Horizontal distance/Depth of point)^2)^(3/2)). Vertical stress at a point is the stress acting perpendicular to the surface, Depth of point at which stress acts, measured vertically downward from surface and Horizontal distance from projection of surface load P to point at which stress is acting.
How to calculate Total Concentrated Surface Load in Westergaard Equation?
The Total Concentrated Surface Load in Westergaard Equation formula is defined as the total force acting on the soil surface is calculated using total_concentrated_surface_load = (Vertical stress at a point*pi*(Depth of point)^2)/((1+2*(Horizontal distance/Depth of point)^2)^(3/2)). To calculate Total Concentrated Surface Load in Westergaard Equation, you need Vertical stress at a point z), Depth of point (z) and Horizontal distance (r). With our tool, you need to enter the respective value for Vertical stress at a point, Depth of point and 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 Total concentrated surface load?
In this formula, Total concentrated surface load uses Vertical stress at a point, Depth of point and Horizontal distance. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • vertical_stress_at_a_point = ((3*Total concentrated surface load)/(2*pi*(Depth of point)^2))*((1+(Horizontal distance/Depth of point)^2)^(5/2))
  • vertical_stress_at_a_point = ((Total concentrated surface load/(pi*(Depth of point)^2))*(1+2*(Horizontal distance/Depth of point)^2)^(3/2))
  • total_concentrated_surface_load = (2*pi*Vertical stress at a point*(Depth of point)^2)/(3*(1+(Horizontal distance/Depth of point)^2)^(5/2))
  • total_concentrated_surface_load = (Vertical stress at a point*pi*(Depth of point)^2)/((1+2*(Horizontal distance/Depth of point)^2)^(3/2))
Where is the Total Concentrated Surface Load in Westergaard Equation calculator used?
Among many, Total Concentrated Surface Load in Westergaard Equation calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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