Factor of Safety Calculation 4

[DamsInc]

Hello,

I have a question regarding the calculation of safety factors. This is a pretty basic question but is causing me some confusion.

When calculating the safety factor against overturning, how do you arrange the forces in the equation (FS=resisting moments/overturning moments) if the force is acting on an inclined face of (for example) a rigid retaining wall. The way I see it, there are two methods:

1) Always resolve an inclined force into a resisting and overturning moment from its horizontal and vertical components,
2) Use the moment caused by the original force and define it as either resisting or overturning as appropriate.

See the attached file for an example of what I’m getting at. Obviously this is trivial when calculating stresses on the base, but it does have an effect on the acceptance criteria. For this case it is straight forward, but other cases with multiple forces also beg the question if a force’s components cause a “negative overturning moment” or a resisting moment.

It seems that it is correct to break the force into its resisting and overturning components first, but why is the second approach incorrect?

 

[JoshPlumSE]

I was talking overturning stability for the footing in particular. Not the overall stability of the structure (for column buckling or what not). The footing is inherently stable with a load applied at the given eccentricity location.

 

[AELLC]

OK here it is - buggy , DO NOT USE FOR REAL WORK.

It is basically written for UBC 1997, concrete design is USD, and CMU design is ASD.

Wind pressure input is service pressure, allow stresses incr by 1.33

All cells are unprotected, and input cells are light blue.

The definition of a structural engineer: overdesign by a factor of 1.999, instead of the usual 2.

 

[DamsInc]

Ok folks, here is my second attempt. I think this more clearly illustrates my issue.

 

[rb1957]

i think you have 120 kNm restoring moment (from the weight of the dam).

you are unstable if the applied forces have an overturning moment > 120 kNm.

your applied forces have an overturning moment of 17.5-3.1 = 14.4 kNm

if your applied forces were 120/14.4 = 8.33 times their current values you'd be on the edge of collapse ... FS = 8.33

Quando Omni Flunkus Moritati

 

[AELLC]

I think you need to make the decision whether to include the downward, vertical component of the active resultant force vector (what you call F1V and F2V)as providing a resisting moment. That is your choice because engineers have differing opinions there.

The definition of a structural engineer: overdesign by a factor of 1.999, instead of the usual 2.

 

[DamsInc]

Thanks everybody for your input, it was very helpful. The conclusion I can draw is that there is not necessarily one correct way to interpret the forces and that it is very much a case of engineering judgement taking into consideration the nature of the forces being applied.

 

[rb1957]

from AELLC's comment i guess you could say "i don't want to account for the restoring portion of the load". that leaves several interpretations including using the horizontal components only ... FS = 120/84.3 = 1.42


Quando Omni Flunkus Moritati

 

[AELLC]

The dead load of the earth above the heel of an ordinary retaining wall footing is always considered as restoring, but the vertical component of the applied overturning force is a matter of judgment - for instance, RetainPro gives you the choice.

The definition of a structural engineer: overdesign by a factor of 1.999, instead of the usual 2.