# Induced Stress due to Point Loads

### 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 <kaklamanosj@merrimack.edu> and Kyle Elmy <ElmyK@merrimack.edu>

### References

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

### See Also

`stressInducedArea`

,
`stressVertical`

, `stressHorizontal`

### Examples

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)
``` |