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

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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

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##  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)