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PostPosted: Thu Jan 02, 2020 2:13 pm    Post subject: Reply with quote

From rex_alfred

Dear All,

Thanks for the detailed discussion on base pressure calculation of footings subjected to biaxial moments.
In the search for a good paper for implementation of linear soil pressure method with redistributed base pressure, i came across few interesting papers.

1. Determination of Base Stresses in Rectangular Footings under Biaxial Bending - Günay ÖZMEN
2. Analysis of Eccentrically Loaded Rectangular Footing Resting on Soil – A Numerical Approach - Jignesh V Chokshi
3. Analysis of isolated footing subjected to axial load and high biaxial moments and numerical approach for its solution - Bijay Sarkar

These papers have already been extensively discussed in this thread.

I would like to add one more paper discussing the same subject through a different methodology derived from basic concepts.

4. New Iterative method to Calculate Base Stress of Footings under Biaxial Bending - Ibrahim Aydogdu

In my opinion, the method discussed by Aydogdu is by far the simplest to implement on computer.

The stress equation considering that all points of footing are at compression.

Stress equation = F/BL + Mz/Iz*x + Mx/Ix*z

This stress equation becomes the equation of Neutral Axis (NA) plane when stress is zero.

The paper alters this stress equation by adding coefficients a, b, c for stress due to axial load, moment about z axis and moment about x axis respectively.

Stress equation = a*F/BL + b*Mz/Iz*x + c*Mx/Ix*z

The iteration starts with a=1, b=1,c=1, and intersection points of NA with footing edges are calculated if there is tension in the footing.

The force is calculated by double integration of stress equation.
The moments are calculated by multiplying the forces with the corresponding lever arms.

At the end of every iteration the calculated resistance by soil (F*, Mx*, Mz*) are compared to the loads (F, Mx, Mz) applied. If the difference between resistance and force are within allowable limits. The plane formed by the assumed a, b, c is the actual NA plane. Else the iterations are continued by altering a, b, c and thus changing the position and orientation of NA plane.

This method is independent of the shape of the contact area of footing.

I felt like updating the thread with this nice  paper published in 2016.

Hope it is useful for the community.

Wish you all a very happy year 2020.

Rex Alfred
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