Omega Factor and Anchorage per ASCE 7-10 Ch. 13

[Nor Cal SE]

I believe this issue has previously been discussed to some extent, but those threads are now closed. I'm interested in getting other engineering opinions about an issue that has nagged me for awhile: omega factor and its relations to concrete anchor bolts per ASCE 7-10 Ch. 13.

The footnote at the bottom of Table 13.6-1 indicates omega must be applied for design of anchor bolts, clear enough on the surface. My question is WHEN does omega get applied? For instance, say you have a simple piece of equipment, considered a "rigid box" for this discussion. You calculate that the effect of horizontal and vertical seismic loads (disregarding omega) would be counteracted by the resisting moment of the dead load, therefore you have no net tension on your anchors. In fact, even if your box has no anchors and simply rests passively on the concrete slab, it still wouldn't overturn as proven by your calcs, and also wouldn't slide presuming the friction resistance is greater than the sliding load.

However, someone else will contend that omega needs to be applied to the horizontal load as part of the overturning check. This is more conservative, and perhaps was the intent of 7-10 code writers, but I believe it would miss all logic, including the logic of physics. Whether the box overturns or not is strictly a matter of geometry and loads, a stability issue, and any theoretical anchors do not impact the geometry and whether there is theoretical overturning. Imagine for a moment that the box doesn't have anchors into concrete but instead has thru-bolts through a thin slab or a steel beam flange. Per code, there would be no omega applied here. Why would that difference in anchor point type impact whether there is net overturning that needs resisting? My contention is that omega should be applied to the net tension load on the anchor (in the scenario that one exists) and the shear load on the anchor once you've performed the statics to get the real load on the anchors. Prior to this, the anchor hasn't yet come into play. What do other people think? I contend my method more closely captures the intent of "amplification" (applied to component/connection, not to the whole system).

One other issue I see:

If your component is located at ground level, most likely your Fp-min equation will govern. The exception would be if you apply omega to the standard Fp, which otherwise was lower than Fp-min, it might now climb higher than Fp-min. Do you go with that load? Or do you take your Fp-min load and apply omega to that (an even more conservative result)? Table 13.6-1 implies that Omega is used in conjunction with ap and Rp factors, and those factors aren't even in play for Fp-min equation.

 

[JStephen]

In the tank world, the omega-factor is not generally used explicity, but the idea is incorporated into the design codes.
The need for anchor bolts, the sizing of anchor bolts, and the sizing of the foundation to which the anchor bolts attach are all based on the nominal seismic load. General seismic loads in the shell and the foundation are based on nominal seismic loads.
The design of the anchor chair, design of the shell for the anchor forces, and the embedment design for the anchor in the concrete are all based on an increased force which is essentially incorporating the omega factor. It is assumed that in a design seismic event, the anchors WILL yield unless considerably oversized.
The R factor is lower for a tank without anchors, so the nominal seismic load is different for the two cases.

 

[JAE]

You calculate that the effect of horizontal and vertical seismic loads (disregarding omega) would be counteracted by the resisting moment of the dead load, therefore you have no net tension on your anchors.

Keep in mind that your calculated seismic loads includes a reduction factor, R, which is not necessarily the true seismic load. You've been allowed to reduce the true seismic load by the factor of "R" to account for the ability of your system to absorb energy, remain ductile, etc. The true seismic demand (your calculated E x R) is much higher - and the Omega factor helps ensure that your brittle, rigid anchors won't fail first.



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[bones206]

Section 13.4 explicitly requires components to be positively attached, bolted, welded, etc. to the supporting structure. So that makes stability checks a moot point, because you know you have to anchor it regardless. If the supporting structure is concrete, that footnote in Table 13.6-1 directs you to the load combos to use IF you are designing the anchors with omega. You just apply those combos to determine anchor demand. If you end up with zero net tension, just design the anchors for the shear demand. You aren't allowed to consider friction resistance for components, so there will always be shear demand.

Bear in mind that designing the anchor with omega is not mandatory. ACI 318 has a few different options for designing anchors for seismic loads besides the simple omega factor option that is used most commonly. If you choose the omega option, then you obey the footnote and use those load combos in Section 12.4.3. If you choose one of the other non-omega options, the footnote doesn't apply and you can ignore it. It's a little confusing from a code standpoint because the design method chosen in the reference standard (ACI 318) determines whether a footnote in the main code (ASCE 7) applies or not...

They added a clarification in ASCE 7-16 Section 13.3 regarding the non-application of omega to the calculation of Fp:

The overstrength factor, Ω[sub]0[/sub],in Table 13.5-1 and Table 13.6-1,is applicable only to anchorage of components to concrete and masonry where required by Section 13.4.2 or the standards referenced therein and shall be applied in accordance with Section 12.4.3. The redundancy factor, ρ, is permitted to be taken as equal to 1, and the overstrength factors in Table 12.2-1 need not apply.

So calculate Fp by itself and only apply omega in the load combinations.