Resistance to overturning for towers

[RobTrans]

The topic is a question about raft/mat foundation for steel lattice towers.
Raft foundations should resist the overall overturning moment of the tower by a factor of safety of 1.5 (depending on the spec). For a rectangular raft we should satisfy (ex/bx)^2 + (ey/by)^2 <= 1/9 to meet the factor of 1.5.
I am looking for a reference to the formula above where it show the working from first principles, so i can understand how to adjust the formula to cater for diffent safety factors.

 

[ishvaaag]

1st try

let ex=bx·k

worse case, safety against overturning in XX plane, bx and ex in such plane

SFOverturning=1.5=
Resisting moment/acting moment=
(0.5*bx-k*bx)*P/(k*bx)*P

divide everything by bx and P to get k=0.2

i.e. the eccentricity of must not exceed 0.2·bx (width of footing along XX.

The eccentricity must be less than 0.2 the width in both planes. If violated in one, it doesn't pass this orthogonal overturning test.