Total Concentrated Surface Load in Westergaard Equation Calculator

✖Vertical Stress at Point is the stress acting perpendicular to the surface.ⓘ Vertical Stress at Point [σ_z]			+10% -10%
✖Depth of Point at which stress acts, measured vertically downward from surface.ⓘ Depth of Point [z]			+10% -10%
✖Horizontal Distance from projection of surface load P to point at which stress is acting.ⓘ Horizontal Distance [r]			+10% -10%

✖Total Concentrated Surface Load is the value of force applied on the surface.ⓘ Total Concentrated Surface Load in Westergaard Equation [P]

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Formula

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Total Concentrated Surface Load in Westergaard Equation

Formula

`"P" = ("σ"_{"z"}*pi*("z")^2)/((1+2*("r"/"z")^2)^(3/2))`

Example

`"50.53583N"=("1.2Pa"*pi*("15m")^2)/((1+2*("25m"/"15m")^2)^(3/2))`

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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 Point*pi*(Depth of Point)^2)/((1+2*(Horizontal Distance/Depth of Point)^2)^(3/2))
P = (σ_z*pi*(z)^2)/((1+2*(r/z)^2)^(3/2))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Total Concentrated Surface Load - (Measured in Newton) - Total Concentrated Surface Load is the value of force applied on the surface.
Vertical Stress at Point - (Measured in Pascal) - Vertical Stress at Point is the stress acting perpendicular to 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

Vertical Stress at Point: 1.2 Pascal --> 1.2 Pascal 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

P = (σ_z*pi*(z)^2)/((1+2*(r/z)^2)^(3/2)) --> (1.2*pi*(15)^2)/((1+2*(25/15)^2)^(3/2))

Evaluating ... ...

P = 50.5358277431387

STEP 3: Convert Result to Output's Unit

50.5358277431387 Newton --> No Conversion Required

FINAL ANSWER

50.5358277431387 ≈ 50.53583 Newton <-- Total Concentrated Surface Load

(Calculation completed in 00.004 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< 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))

Total Concentrated Surface Load in Westergaard Equation Formula

Total Concentrated Surface Load = (Vertical Stress at Point*pi*(Depth of Point)^2)/((1+2*(Horizontal Distance/Depth of Point)^2)^(3/2))
P = (σ_z*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 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 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 Point (σ_z), Depth of Point (z) & 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 -> 0.002717 = (1.2*pi*(15)^2)/((1+2*(25/15)^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 = (σ_z*pi*(z)^2)/((1+2*(r/z)^2)^(3/2)) or 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 is the stress acting perpendicular to 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 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 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 Point (σ_z), Depth of Point (z) & Horizontal Distance (r). With our tool, you need to enter the respective value for Vertical Stress at Point, 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 Total Concentrated Surface Load?

In this formula, Total Concentrated Surface Load uses Vertical Stress at Point, Depth of Point & Horizontal Distance. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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