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# Re: FOS for Overturning

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: FOS for Overturning
• From: <BRBATES(--nospam--at)aol.com>
• Date: Thu, 25 Jun 1998 12:16:14 EDT

```<< Assume the footing is 15 kips in weight and is 8'x 6' x 2' thick. Pardon
the
<< phony graphics, I am using AutoBadd.
<<
<<
<<             ^ 10k
<<             |
<<             |
<<      ------> 3k
<<      ---------------
<<      |             |
<<      |             | 2'
<<      |             |
<<      ---------------
<<            8'
<<
<<
<<
<< 2.	Assuming you do think it should be included as an overturning force,
would
<< the correct calcualtion be Movtg = 3x2 + 10x4 = 46 and Mstab= 15x4 = 60,
<< therefore FS = 1.304   OR is the correct one: Movt = 3x2=6 and Mstab=
<< (15-10)x4=20  FS = 20/6 = 3.333.  By definition, it would appear that the
1.3
<< answer is correct and that algebraically adding common forces is not
<< permitted.

It's not obvious to me that algebraically adding common forces is not correct.
For example, isn't the 10K uplift force actually a summation of several
forces? In reality it probably would be, for example, a combination of DL and
WL. Let's say the 10k uplift is actually a 12K uplift wind load combined with

OTM SF = (15X4 +  2X4) / (12X4 + 3X2) = 1.26

In my opinion, to calculate OTM you should first sum same direction loads
acting simutaneously at a common location and then use the resulting moment
for the calculation, so the calculation should be:

OTM SF = (15-10)X4 / 3X2 = 3.33

Note that even if we use the 12k and 2k representation for the 10k uplift,
we'll still get the same OTM SF.

Another way to look at it: the 10k uplift cannot cause overturning on its own
(when applied in the center), it can only reduce the footing's ability to
resist overturning.

My 2 cents worth.

Bruce Bates
RISA Technologies

```