Influence factor from Boussinesq

[scottiesei]

There is an influence factor to determine the stress below a corner of a rectangular area which is derived from Boussinesq's equation. The format is a large equation of m and n, then an arctan. There is a modifier for when the arctan portion of this equation is negative. Does anyone know what the modifier is? I know this is vague but I am hoping that I have included enough information that someone familiar with the topic would be able to understand.
Thanks.
SS

 

[civilperson]

No modifier shown in the equation as printed in Das text, Principles of Geotechnical Engineering. Page 196 of Second Edition. The arctan of a negative quantity is negative.

 

[jdonville]

scottiesei,

I know Taylor has it in his (old) book. I don't have it handy at the moment, but will try to get for you shortly.

Jeff

 

[jdonville]

scottiesei,

Taylor's formula does not use arctan.

Taylor's second term is:

arcsin((2*m*n*((m^2+n^2+1)^0.5)) / (m^2+n^2+1+m^2n^2))

Note that the denominator is always positive. The angle (expressed in radians) is less than pi/2 when m^2+n^2+1 is greater than m^2n^2, otherwise the angle is larger than pi/2, but less than pi. You may need to make suitable corrections based on the magnitude of the returned angle.

Coduto presents a similar approach.

Jeff

 

[BigH]

See Poulos and Davis' book "Elastic Solutions for Soil and Rock Mechanics". Almost all such formula are well documented.