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RE: steel - vibration analysis

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Jordan - 

1) Allen's message essentially said that it was impossible to have vibration
problems in non-orthognal areas of a building.  The main point of my
response was that this stance of his was patently absurd. I take it that you
at least partially agree with me on that.  

2) Please take a closer look at that example in 7.2 of Design Guide-11. Your
characterization of that problem is COMPLETELY inaccurate. I'm not trying to
flame you here... I just think you didn't read the example very closely. The
text of that example actually says the following:
"Unacceptable walking vibrations occurred throughout most of the floor, more
so adjacent to the atrium".  

When you look at the figure, the area adjacent to the atrium is the one with
the non-orthogonal framing.  Now, look closer at the skewed girders.  They
added in new COLUMNS at the mid-points of the girders.  That's a waaay more
significant stiffening effect than what they did to the other girders.
Personally, I'm confident that our RISAFloor program would produce results
which show the skewed area being more sensitive to vibration than the rest
of the floor.


3)The fact that you characterized non-orthogonal plate vibration as akin to
a "non-linear non-prismatic curved member" is a fairly gargantuan
exageration. Structural vibrations just aren't that complicated.  If it
were, then you'd need a PhD to understand modal analysis, even more so if
you were doing a Response Specta Analysis. I understand that some folks
(perhaps even you) can find vibrations to be a truly intimidating subject.
But, we're talking about common framing configurations with girder to joist
angles of less than 90 degrees. This just isn't that big of a difference.
We're not talking about extending the rectangular panel mode concepts to one
of those freaky Frank Gehry buildings that look like they're melting.

Like you pointed out, a true modal analysis (which RISAFloor can do through
it's interaction with RISA-3D) can be appropriate for many of the funkier
non-orthogonal cases (like the Gehry buildings).  But, doing that for a
nearly orthogonal bay would be a shocking amount of extra work for something
that is almost certainly going to produce the same kind of results as the
DG-11 calculations.


Finally, I said before that I thought that I had read every article that
AISC has published on Floor vibrations. And, I still haven't seen anything
in any of their articles that implies that non-orthogonal areas are immune
from floor vibration problems.  Nor have I seen any warnings or cautions
about extending these concepts into systems that are not perfectly
orthogonal.   But, if I'm missing something important here, then I'd like to
know about it.


Sincerely, 

 
Josh Plummer, SE
RISA Technologies

-----Original Message-----
From: Jordan Truesdell, PE [mailto:seaint1(--nospam--at)truesdellengineering.com] 
Sent: Tuesday, June 12, 2007 4:42 AM
To: seaint(--nospam--at)seaint.org
Subject: Re: steel - vibration analysis

Josh - when I read  Allen's post, I generally agreed with it, though I may
have misread what I wanted to read.  Where framing changes length within a
bay, it is correct that the variation in frequency tends to reduce or
eliminate footfall vibrations because of the large number of different
vibration modes at play - there is no large area in which the vibrations may
be sustained.

The example in 7.2 is also a very regular structure, with the diagonal areas
both on the perimeter and around the atrium apparently not affected by the
vibration problems - the primary areas of stiffening were in back-to-back
regular orthogonal bays.  (I only skimmed the article to see what you were
referring to, let me know if I missed some of it) You can still have issues
in non-orthogonal bays if the primary frequency is related to the girder,
but the joists/beams should tend not to promote resonance unless they are
all of similar stiffness, or all fall in the lousy range. 

Vibrations of plates and shells is greatly complicated by non-regular
geometry, and can effectively only be performed numerically.  If you have an
issue with an unusual structure, the first thing to do (barring obvious
deduction) is to determine your mode shapes, frequencies, and modal mass
participation - then you can start to isolate where the issues are. Your
comparison of extending the vibration theory from wide flange to tube is not
analogous- extending from a wide flange to a non-linear non-prismatic curved
member would be more appropriate. And, of course, the theory doesn't extend
to such members.

(now where did I put that set of nomex khakis...)

Jordan



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