# stressInducedPoint: Induced Stress due to Point Loads In geotech: Geotechnical Engineering

## Description

These functions calculate induced stresses due to a point load applied at the surface: induced.point performs this calculation at a specific depth, induced.point.profile performs this calculation at a series of depths.

## Usage

 ```1 2``` ```induced.point(P, x, y, z, nu) induced.point.profile(P, x, y, z = NA, nu) ```

## Arguments

 `P` point load `x` horizontal distance from point load in the x direction `y` horizontal distance from point load in the y direction `z` depth(s) of interest `nu` Poisson's ratio

## Details

The depth(s) of interest (z) should be a single value for induced.point, and a vector of values for induced.point.profile. For induced.point.profile, the default vector of z values is 1-ft or 1-m increments, to a maximum depth of 50 ft or 50 m.

## Value

Function induced.point outputs a six-element list giving the induced stress at a specified depth using the Boussinesq (1885) theory.

• sigmaX = induced horizontal stress in the x direction

• sigmaY = induced horizontal stress in the y direction

• sigmaZ = induced vertical stress

• tauZX = induced shear stress on the ZX plane

• tauYX = induced shear stress on the YX plane

• tauYZ = induced shear stress on the YZ plane

Function induced.point.profile outputs a seven-element list containing seven vectors that display the depth variation of induced stresses using the Boussinesq (1885) theory.

• depth = depth

• sigmaX = induced horizontal stress in the x direction

• sigmaY = induced horizontal stress in the y direction

• sigmaZ = induced vertical stress

• tauZX = induced shear stress on the ZX plane

• tauYX = induced shear stress on the YX plane

• tauYZ = induced shear stress on the YZ plane

## Author(s)

James Kaklamanos <[email protected]> and Kyle Elmy <[email protected]>

## References

Boussinesq, J. (1885). "Application des Potentiels a L'Etude de L'Equilibre et du Mouvement des Solides Elastiques", Gauthier-Villars, Paris (in French).

`stressInducedArea`, `stressVertical`, `stressHorizontal`
 ```1 2 3 4 5``` ```## Example code for Induced Stress due to a Point Load induced.point(P = 100000, x = 5, y = 2, z = 6, nu = 0.35) ## Example code for Induced Stress due to a Point Load: Profile induced.point.profile(P = 100000, x = 5, y = 2, nu = 0.35) ```