Footing Stability Ratio

[nrjdjjs]

If a soil supported mat supports 4 piers with 2 of the piers subjected to compressive loads and the other 2 piers subjected to uplift loads for a certain load combination, what is the correct way to calculate stability ratio about an edge of the mat?

1. Would the uplift loads contribute to the overturning moment about an edge of the footing or is it just the applied shears and moments on the piers that contribute to overturning?
2. In continuation of 1 above, in calculating resisting moment, is it appropriate to algebraically add all the vertical loads on the piers (both compressive and uplift), add the weight of the piers, footing and the soil and use this resultant load as contributing towards resisting?
3. In general, SR is defined as Mr/Mo where Mr is the resisting moment and Mo is the overturning moment. Would SR = L/2e be correct under all circumstances and equate to SR calculated using Mr/Mo?

Thank you

 

[DaveAtkins]

In recent years, codes have moved away from using a "stability ratio" to check overturning, uplift, etc. The proper way to design is to use 0.6*DL in the various load combinations. Then, either the design works or it doesn't. There is no checking a factor of safety against overturning and/or uplift.

DaveAtkins

 

[nrjdjjs]

Thank you for your response.

Is that true? ACI 336.2R states that overturning must be considered for combined footings and mats.

 

[jayrod12]

Overturning must be considered. But there's no stability ratio like the old working stress days.

 

[Leftwow]

Google Figure 10-3 Distribution of bearing pressures, and go to images. Should be one of the first few images.

 

[mike20793]

Yes, you still need to check overturning. Dave is merely stating that the factor of safety is included in the design load combinations so there's no need to reduce your capacity, etc. to provide a factor of safety. All loads will contribute to the overturning or resist the overturning (unless it acts at the point you're summing moments). Sum moments about a corner of your mat and that's how you calculate the overturning. I would include the weight of the mat but not the weight of the piers or the soil since it is supporting the mat in your overturning calculation.

 

[nrjdjjs]

Does that mean that if appropriate load combinations with 0.6DL etc. are considered for soil stability calculations then in checking overturning, all that needs to be checked is that the resisting moment >= overturning?

 

[jayrod12]

Correct. The safety factor is baked into the load combinations.

 

[nrjdjjs]

Section 4.3 - Overturning calculations in ACI 336.2R (Analysis and Design of Combined Footings and Mats) still states that the stability ratio should generally not be less than 1.5. Is this because this publication has not been updated in lieu of the above discussion regarding using appropriate load combinations such as 0.6DL or am I missing something?

Thank you all for your responses.

 

[jayrod12]

Using that stability ratio you would get to account for 100% of your dead load as resisting. Or you use 0.6D and check against unity.

 

[mike20793]

The proper load combinations are outlined in ASCE 7 which references the ACI documents, not in the actual ACI document. Typically, we overestimate the dead load to be conservative for gravity loads, so you should really be using 90% of your dead load (see LRFD combinations). The 1.5 safety factor comes from 0.9/0.6=1.5. That's how it's baked into the combinations.

 

[KootK]

1. Would the uplift loads contribute to the overturning moment about an edge of the footing or is it just the applied shears and moments on the piers that contribute to overturning?

Definitely the uplift would contribute.

2. In continuation of 1 above, in calculating resisting moment, is it appropriate to algebraically add all the vertical loads on the piers (both compressive and uplift), add the weight of the piers, footing and the soil and use this resultant load as contributing towards resisting?

I'll include any resisting load that I'm confident will be present during whatever environment will create the overturning tendency. I'll take foundation weight, piers, columns, structural walls, soil, slab on grade... I won't include live load, snow load, equipment, or architectural finishes with the rare exception of where those things are actually the cause of the overturning.

3. In general, SR is defined as Mr/Mo where Mr is the resisting moment and Mo is the overturning moment. Would SR = L/2e be correct under all circumstances and equate to SR calculated using Mr/Mo?]

The e<L/2 business should still apply in principle if you do it like this:

1) e must include all load effects.
2) apply your load factors as discussed above.
3) instead of e<L/2 just determine whether or not your aggregate eccentric load still lands on the footing.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[nrjdjjs]

Thank you all for your responses.

The attached pdf shows 2 different methods of calculating overturning moments and resisting moments for the same foundation loads and geometry. It seems that both of these methods are being used. Which method is the correct way to calculate overturning moments?

 

[DaveAtkins]

Method 1 is a check of overturning. Method 2 would be used to determine bearing pressures under the footing, due to the applied loads.

I would not use either method. I would check the footing for the various applicable load combinations per code (you don't show what load combination has yielded the P loads). As I said before, if the footing is not overturning assuming 0.6DL, then stability is satisfied. But the load case with 0.6DL may or may not give you the highest bearing pressure.

DaveAtkins

 

[nrjdjjs]

So let's say we have two unfactored load combinations 1. DL + WL and 2. 0.6DL + WL. In either case is overturning considered satisfied as long as resisting moments >= overturning moments without regard to the actual ratio of the resisting moment to overturning moment?

 

[DaveAtkins]

For overturning, I can't envision how DL + WL would ever control over 0.6DL + WL. But to answer your question, when you check the 0.6DL + WL combination, the FS against overturning is built into the load combination. Or "baked" into the load combination, as "Chef" jayrod12 would say

DaveAtkins

 

[mike20793]

You should be referencing the pertinent building code for design load combinations. In ASCE 7-05 the uplift combination is 0.6DL + 1.0WL but it changed to 0.6DL + 0.6WL for ASCE 7-10 since the wind limit state was changed. You also need to examine every load combination and design for the worst case.

My previous post explained how the safety factor is included in the combination.