Bearing pressure for rectangular footing double eccentricity 4

[LR11]

I found this graph (see attached Fig 6.14-d) from another post.
It's for estimating footing bearing pressures when effective load is outside the kern.
Has anyone come across formulate to use instead of reading from graph.

Curves are from American Railway Engineering Association.

 

[milkshakelake]

The formulas are in the attachment you provided. q = Q/A times some things. I use those instead of a graph because it's easy to put into a spreadsheet.

I rarely use purely eccentric footings. It's hard to get it to work because the kern is so small. I use grade beams to neutralize the eccentricity these days. Though I suppose it could work for a 1-2 story building.

I think a good exercise is to derive the formula for eccentric footing by yourself. It's easier than it looks. It's just a matter of doing the triangular distribution and using force equilibrium. You can do a lot with that. Edit: Sorry, just reread your post. This thought only applies for single axis.

 

[Celt83]

for general biaxial bending it’s a bit tricky you could generate formulas for a fixed shape foundation but the effort may not worth it.

See this thread: https://www.eng-tips.com/threads/combined-footing-outside-of-middle-third.476601/

 

[HTURKAK]

This is an old graph for this subject Year 1927.. President Calvin Coolidge era. From the book FOUNDATIONS OF STRUCTURES ( By DUNHAM , 1960)
IMO, the best option is to shift the footing if possible so that the resultant load acts within the kern.

 

[icebloom]

The complete analytical solution is quite complex. It can be found in the linked article:

https://www.researchgate.net/publication/312362987_Complete_Analytical_Solution_for_Linear_Soil_Pressure_Distribution_under_Rigid_Rectangular_Spread_Footings

 

[LR11]

Thanks all for responding.
The link in icebloom’s post looks like it could be what I was looking for.

1. For context, footings were such that plinth had to be near a corner. And the eccentricity was going to assumed as below (ex & ez from bending, and Ex & Ez from geometrical offset of plinth).



2. The first time I looked at pressures outside of kern was as a graduate. Can’t recall the details but have documented formula shown below. Had written down (looks like incorrectly) that it came from reference: Esling FK, A Problem Relating to Railway Bridge Piers of Masonry or Brickwork, Paper No. 3592.
Compared K value to attachment in original post, but values were different.
I can't trace where formula below came from. Maybe specific to some geometry and loading?