Seismic Combination Question

Refering to Example 26 in SEAOC Vol 1 2009 pg. 102

Could use some expert clarificaiton...

When calculating the required strength for a column, overstrength required, they subtract Ev from Emh per ASCE 12.4-6, and then subract Em from 0.9D per ASCE 2.3.2 yielding tension of 205kips.

However, using ASCE 12.4.3.2 eq 7. yields 223 kips by subracting Ev from 0.9D first.

Which is correct or what am I missing? Is Ev supposed to reduce the overall seismic effect as it does in their example? Or should Emh be +/- and they missed it?

Thanks in advance.

I'm using LRFD for both, and both are within 12.4 section of ASCE.

Given:

Sds = 1.1

D = 40 kips

QE = 100 kips

Overstrength = 2.5

SEAOC does this...

Em = Emh - Ev = (2.5)(100) - 0.2(1.1)(40) = 241.2kips (eq 12.4-6)

then...

0.9D - Em = 0.9(40) - 241.2kips = -205.2 kips (using combination 7 in 2.3.2)

When I, and I'm sure many of you, get a seismic combination question I go directly to 12.4.3.2 basic combinations where for the same numbers...

(0.9 - 0.2Sds)D + Overstrength*QE = 0.68(40) + 2.5(-100) = -222.8kips

I think your procedure is correct and SEOAC is in error. The way I read ASCE 7 is that 12.4.3.2 load combinations SHALL be used when overstrength is considered. I would hope that an essay question grader would recognize the situation and give full credit. If this issue arose over a multiple-choice question and the answer was incorrect, I would hope the question would be thrown out and not counted against an examinee. It's difficult to thoroughly and accurately edit these documents and I think this one just slipped by SEAOC. I found mistakes of this sort throughout my preparation and made note of why I thought they were wrong and what I considered correct.

This issue brings up a provocative issue in our profession. We have research and design materials that allow us to design members to a high degree of accuracy, but our uncertainty w/r/t loads is usually at least an order of magnitude greater. I consider loads conservative and I will design members with capacity as close to demand as I can get. I know plenty of people who are uncomfortable with the uncertainty in the loads and they pad their designs with heavier members as a result. The reality is that either structure is susceptible to failure but neither is likely to fail. When it comes down to it, that's the best that I think we can do...produce a design that is extremely unlikely to fail.

I saw that SHALL as well which leads me to believe I'm right in using 12.4.3.2 but I still feel like I'm missing something. If SEAOC is in error, I can't articulate what that error is because they are using exactly what's out of 12.4.3 as written.

Yes, this is a mistake in the SEAOC Blue Book. I caught it myself when studying this fall, and have verified with one of the editors that it was an error and has been corrected in the latest versions. They make that same mistake in at least one other problem. The +/- is the issue. You want the combo that's going to give you the worst case. So that's usually (0.9-0.2Sds) and (1.2+0.2Sds). They just got mixed up with the double subtraction.

I see, so where in the ASCE 12.4.3 equations should the +/- go?

i.e.

Shouldn't equation 12.4-5 and equation 12.4-6 be the same Em = Emh +/- Ev ? Or even Em = +/- Emh +/- Ev ?

the +/- apply to the omega naught times Q sub E. the intent of combination 7 is to reduce gravity load and apply the maximum lateral load to produce uplift - i.e. the opposite of the gravity load. see the commentary to chapter 2 which will include a statement similar to this one, "Load combinations 6 and 7 apply specifically to the case in which the structural actions due to lateral forces and gravity loads counteract each other."

So in the governing load combination (here, given by 12.4.3.2 eqn 7) you have to consider the 0.9D load term as acting in the opposite sense of both the 0.2SdsD and the omega naught times Q sub E to be in accordance with the intent of the load combination, i.e. that gravity effects and lateral effects counteract each other.

12.4-5 and -6 are basically combining 12.4-4 and the load combos in 12.4.2.3. They're just explaining there that when you use 1.2D, you should add Ev, and when you use 0.9D you should subtract Ev. The idea is that you are "worsening" the effects of DL with the vertical EQ load. So if DL is amplified by 1.2, make it worse by adding more downward load (Ev) and then add the worst case downward EQ load (worst case for compression). If DL is lessened by 0.9, make it worse by subtracting vertical load (Ev) and then add the worst case upward EQ load (worst case for tension).

It sounds like from your earlier posts that you understand the concept, and sometimes that's more important that explicitly writing out the combos with double negatives or whatever.

I see, so if we apply that to the example what SEAOC should have done is add the +/- ahead of Emh (omega naught times Q sub E) so that

Em = - Emh - Ev = - (2.5)(100) - 0.2(1.1)(40) = -258.8kips

And should have left the '+' sign alone in combo 7, 2.3.2 so that

0.9D + Em = 0.9(40) + (-258.8) = -222.8 kips

Therefore yielding the worse case tension.

This has been a helpful conversation.

Topics like this are why I'm a firm supporter of SE licensure - the process of preparing for and passing the examinations makes us study codes and think about applications which are steps toward our becoming better engineers.

Success in structural engineering (and many other aspects of life) comes down to two skills: reading and thinking. I have been astonished at the lack of code knowledge demonstrated by many in our profession, oftentimes (in my opinion) attributable to the fact that many engineers never bother to read the codes and/or understand how to apply them. As Hans Reichenbach so wisely said, "As long as error is recognized as such when it is encountered, then the path of error is the path to truth."