Eccentrically Loaded area supported on 4 piers 1

[Pete1919]

Hello all,
I need help please. I have 6'(say, x-axis) x 4'(Y-axis) area with a point load of 100 tons acting 2' from short neutral axis (ex = 2') and 1' from long neutral axis (ey=1). The area will be supported on four (4) piers. What will be the load distribution on 4 piers? Weight of the pad (area) will be ignored.

I calculated moment and calculated stresses at 4 corners using p/A+/-Mx/Ix*y +/-My/Iy*x. I interpolated stresses at mid-points between corners. Stress at center would be 100/24=4.17 tsf. Then I assigned tributary areas (four quadrants) to each pier. Took "average" stress for the quadrants multiplied by quadrant area of 6 sq.ft to get pier loads. The pier loads were 69, 31, -19 and 19 tons.

Using different method of 25+/-My/(6*2) +/- Mx/(4*2), I came up with the pier loads of 54, 29, -4, and 21 tons.

I am trying to find which method and answer is correct. Any comments or calculation will be appreciated. Thanks.

 

[hokie66]

One final shot...about the force directly at the corner. If the corner pile reaction is not equal to the applied force, then that means there is a portion of the load, in the above case 25%, carried in bending of the cap. How do we know there is compatibility without knowing anything about the pile and cap other than horizontal dimensions? This leads me to think that the approach (as well as mine), is approximate with limited eccentricity, but when taken to the extreme, it is not reliable.

 

[rapt]

Hokie66,

Yes, it is not accurate. It is giving an estimate of the distribution of the forces assuming the factors I mentioned earlier are satisfied and there is no moment connection between the piles and the pile cap and probably some other variables.

You could do something far more accurately if you modelled it as a 3D frame but then you need to know the pile lengths, the accurate achievable soil pressures under each pile, skin friction for each pile etc. None of which you know at design time and probably not even during construction.

So the 2 extremes of the answer are your initial solution with 100% in the pile directly under the column, and the distributed load answer with compression and/or tension loads in each pile.

A sensible engineer would design each pile for the worst case from both methods, which I think Kootk agrees with above somewhere. But then a sensible engineer probably would not have a 4 pile group with the column above lined up on one of the piles except in an extreme case!