Help with Shear and Moment Diagram for combined foundation with bi-axial loads 1

[XinLok]

I am designing a Combined foundation with 2 pedestals P1 & P2.

I am trying to draw the Shear and Moment Diagram and still confused about the vertical forces how to include it in the Shear diagram.
Pressure under Foundation is p1, p2, p3 & p4.

Volume of pressures under Footing = (p1 + p2 + p3 + p4) / 4 * Length Foundation x Width Foundation

if Fx1 & Fx2 = 0 or Fx1 + Fx2 = 0 then Fy1 + Fy2 = Volume of pressures under Footing.

I can draw properly the Shear Diagram only if Fy1 + Fy2 = Volume of pressures under Footing.

if Fx1 & Fx2, then the values of p1 + p2 + p3 + p4 will be changed and then the volume of pressures under foundation will be changed.
if so, I won't have Fy1 + Fy2 = volume of pressures under foundation

Please help, I stuck for months with this trying to draw shear diagram when ever Fx, Fy and Fz exist.

I search all book and you tubes trying to find a combined foundation examples with biaxial moment and forces and found nothing.

 

[Celt83]

I struggle with this one as well.

A few assumptions:
- Soil bearing pressure varies linearly on any edge
- Corner Pressures are known
- Plane sections remain plane
- The foundation may be represented as an equivalent beam section at any section cut.

From a pure statics perspective you can cut sections a various intervals and form a shear, moment, and torque at the centroid of each section to satisfy equilibrium. From this approach the shear diagram only requires you know the resultant of the 3D parrallelepiped of pressure and not necessarily the location. The moment and torque would require you to know the resultant location in space.

 

[Celt83]

for determining the Resultant of the pressure, volume of the parallelepiped, and the moments about each axis refer to my response to your post regarding the numerical solution for the biaxial bearing pressure the resulting integrals are of the same form: Link

 

[Celt83]

Another very important note the above relies on an overarching assumption that the foundation is rigid compared to the soil otherwise you need to fall to an FEM solution to account for the foundation flexibility the soil springs.