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Re: FOS forOvtg clarification

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Here are the examples I promised to give.

Test conditions:

We have a concrete ftg 8 ft long and 2 ft high. For simplicity, it is sitting
on a concrete slab with no frictional resistance. On the right end(called
point "O") is a steel angle bolted to the slab to resist sliding of the
footing but will not keep the footing from lifting up. The footing dead wt is
15 kips located at the center.

Required:

What is the Factor of Safety against overturning (F.S.) about point "O" due to
various loading.(This is too vague, we should ask for the Factor or Safety
against instability  of the footing due to all combination of external forces
and resisted only by the ftg dead wt.)

Case 1: 3 kips horiz load at top towards the right.

Moments about point "O":

OM=3x2=6 kip-ft
RM=15x4=60 kip-ft
F.S. aginst oveturning  about poiunt "O"=60/6=10(assuming we use actual dead
load for resisting and not 2/3 DL or whatever)
If the slab is strong enough to carry the vertical load of the footing and the
steel angle and its connection to the slab is strong enough to resist the
lateral load, then the system is stable.

Case 2: 10 kips uplift at center.

No overturning about point "O".
Net vertical load is downwards= 15-10 =5 kips at center.
F.S. against uplift=15/10=1.5
If slab can carry this net vertical load, the system is stable.

Case 3: 20 kips uplift at center.

Still no overturning about point "O". 
Net vertical load is upwards= 15-20=-5 kips at center.
The footing is not connected  to the slab so it lifts up.......the system is
unstable.
No overturning about point "O".

Case 4: 3 kips horiz load to  the right and 10 kips uplift at center.

Moments about point "O":

OM=3x2=6 kip-ft
RM=(15-10)x4=20 kip-ft( from case 2, the 10 kips uplift does not create
overturning about point "O" but only counteracts the 15 kips vertical dead
load of the footing)
F.S. against oveturning about point "O"=20/6=3.33
F.S. against instability(lifting and overturning, at the same time)= ??????
Maybe we cannot combine lifting and overturning instability calculations at
the same time. We can get the average of the two Factor of Safeties and if it
is within your alloable, Its OK. Or we do it separately. If any one of the
F.S. is not acceptable, the whole thing is not acceptable.

Case 5: 10 kips uplift 1 ft to the right of the center.

Check stability of the system:

15 kips downward at center  and 10 kips upward 1 ft to the right, the system
will tend to rotate but since the net vertical force is greater downward and
the system is tending to rotate counterclockwise, the botom left end of the
footing is putting some load the slab. system will stabilize as long as the
slab can resist this load. 

No overturning abount point "O".
Check F.S. against rotation about the left side at the bottom:(not at point
"O")
OM=10x5=50 kip-ft
RM=15x4=60 kip-ft
F.S. against rotation=60/50=1.2
F.S. against uplift=15/10=1.5

Case 6: 3 kips horizontal load at top and 10 kips uplift 1 ft to the right of
the center:

Check combination of Cases 1 and 5:

F.S. against overturning about point "O"=10.0
F.S. against rotation=1.2 (No Good, less than 1.5)
F.S. against uplift = 1.5

System is no good.

You could try different load combinations and  location and different sources
of external  loads destabilizing loads and restoring loads, The point is
Define what F.S. you want and what is allowable.

Ernie Natividad