Steel SCBF, inverted chevron brace-beam connection

[DETstru]

I'm doing an example problem from the NCEES SE practice exam book. It is a steel beam with two SCBF brace connections below at it's mid-span. No braces above. They are asking what the max vertical earthquake load in the beam is from the braces.

When lateral loads to the frame are induced, one brace will be in tension while the other is in compression.

According to AISC, you use the expected strength in tension from one brace (Ry*Fy*Ag) minus the expected post-buckling strength in compression from the other brace (0.3*1.14Fcre*Ag, where Fcre is like Fcr but calculated with RyFy instead of just Fy).

The solution to the problem uses the Ry*Fy*Ag method for tension, but it simply pulls the capacity from the Steel Manual tables for compression. It doesn't use the expected strength derived from Ry and Fcre to determine capacity in compression. This wrong according to all the examples I've found in AISC, NEHRP, and the SEAOC seismic design manual.

Scans linked:

http://i.imgur.com/2hDDf9P.png

http://i.imgur.com/SjvWgqk.png

Anyone have any thoughts on this? Maybe there is an exception that I'm not aware of?
Thanks

 

[Deker]

Don't think you are missing anything. In practice I don't mind using the simplified 0.3Pn in order to use the Manual tables to speed up the design, but I would expect more rigor from an exam question.

There is a bit of an inconsistency with this part of the code in my opinion. OCBF requires the post-buckled compression strength of the brace be assumed as 0.3Pn, while SCBF allows anywhere from zero to a maximum of 0.3 times the expected brace strength in compression. Since the post-buckled strength of the brace only reduces the demand on your capacity-protected elements, I would think it more prudent to use 0.3Pn rather than 0.3 times the expected strength, which assumes zero out-of-straightness and an upper bound Fy. I would like to say that's already baked into the 0.3 factor that gets applied to the expected brace strength, but since the 0.3 factor is also applied to Pn for OCBF I'm not so sure.

 

[Shu Jiang PEng SE]

The expected strength in compression could be taken as the lesser of RyFyAg and 1.14FcreAg. However, another requirement needs to be satisfied: the expected post-buckling brace strength shall be taken as a maximum 0.3 times the expected brace strength in compression.

The second requirement will pose more strict strength requirements on the beam, therefore, 0.3FcreAg should be used for the brace in compression.

 

[DETstru]

Deker, I agree about the shorthand method. It's definitely easier to just pull a value from the table but I wouldn't expect that from an exam question as you say.

Xian, post buckling strength is defined as 30% of expected strength in compression. The expected strength in compression is 1.14FcreAg, therefore, post buckling strength is 0.3*1.14*Fcre*Ag as defined in ASIC 341.
The issue is that the exam question solution didn't do any of this. They simply used 0.3FcrAg (note that this is Fcr, not Fcre). While it is conservative, this method is not indicated anywhere in AISC 341 and makes a multiple choice question very difficult to answer correctly.

 

[KootK]

Yeah, when it comes to the exams, you just gotta roll with what you think is right-est and move on. I believe that they give some account to questions that wind up confusing a lot of test takers in their scoring adjustments.

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.