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More problems with the 1997 UBC

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For those of you who are interested...

Here's a good example of how to use the 1997 UBC for equipment design.  If
you choose to accept the challenge, I urge you to run an independent
calculation by yourself to see what answer you get...  Then compare it to my
solution, which has been independently checked by two other structural
engineers.


PROBLEM:

I have a client who wishes to hang a 800 pound piece of equipment from the
ceiling somewhere in an existing 30 story building.  For what lateral force
should I design it, using the 1997 UBC and Allowable Stress Design (ASD)?

Given:

Zone 4, Soil Type D, no near field effects, life-safety equipment

Ca = 0.44
Ip = 1.5







SOLUTION:

Using Equation 32-1:

Fp = (4 * 0.44 * 1.5 * 0.8 kips)/1.4  = 1.51 kips (1.88 g)

That seems like an awfully large force for a piece of equipment hanging from
a ceiling.  This equipment is suspended less than two feet below the
concrete floor slab...  It seems really unlikely that the equipment needs to
be elastically designed for accelerations this large.  Note that if we had
been located near a Type A Fault, the design accelerations would have been
another 50% larger!


Maybe I can use the more complicated, but more "rational" formula, Equation
32-2, which should give me a lower design force, correct?

ap = 1.0 and Rp = 3.0 (equipment hung from ceiling)

And since my client would like to place this equipment on each floor and
would like one single design, rather than a separate design for each floor,
hx/hr = 1.0

Fp = (1.0 * 0.44 * 1.5 * (1 + 3*1.0)/3.0 * 0.8 kips) / 1.4 = 0.50 kips (0.63
g)

Which isn't too bad...

But wait, since this equipment has vibration isolators, ap = 2.5 and Rp =
1.5, per footnote 14, which I almost missed!  (There are so many footnotes
that they take up almost a page themselves, even when formatted in a really
small font!)

Fp = (2.5 * 0.44 * 1.5 * (1 + 3*1.0)/1.5 * 0.8 kips) / 1.4 = 2.5 kips (3.13
g)

Which is much higher than the simple equation 32-1...

There's also another provision in footnote #14!

Since I have to hang this from the ceiling, I have to use either expansion
anchors or shallow anchors, so the forces for the connections are doubled
(ap = 5.0).

Fp = 5.0 kips (6.25 g).

Even if I am only at midheight in the building, the "rational" formula
design force is far grater than that produced by the simple formula.

It seems that the dynamic and supposedly rational formula 32-2 can break
down fairly quickly and that I am reduced to designing this equipment for
1.88 g.  

BUT WAIT!  This footnote #14 to Table O, which is ONLY referenced by
Equation 32-2, back-references Equation 32-1 and requires me to further
double my forces for the anchors, even if I use only Equation 32-1.  This is
an incredible error in the code, since I never had to use Equation 32-2 (and
consequently Table O) in the first place!  Unless I tried to use the
"alternate" procedure, I would never even know that the code requires me to
double the forces yet again...


THEREFORE, the design force for the anchors for this equipment must be
designed for 

Fp = (4 * 0.44 * 1.5 * 0.8 kips) * 2.0 /1.4 = 3.02 kips (3.77 g)

Since connections typically have a factor of safety of at least 3, this
equipment should be good for at least 11.31 g.  What a relief!  I was really
concerned that this equipment, hung less than two feet from the underside of
a slab in a 30 story building was going to experience accelerations of that
magnitude!

If the building had been located within 2 km of a Type A fault, I would have
to design for 5.66 g and the equipment would be able to withstand 16.97 g.


For comparison, the forces in the 1994 UBC would only be

Z = 0.4
Cp = 0.75 * 2 (Non-rigid equipment)
Ip = 1.5

Fp = 0.4 * 0.75 * 2 * 1.5 * 0.8 kips = 0.72 kips (0.90 g).

Which means that the equipment should be able to withstand 2.7 g.


For this example, the 1997 UBC forces are more than four (or six, depending
on location) times larger than the design forces of the 1994 UBC!


Based on this example and a number of other similar examples, here are my
conclusions regarding the 1997 UBC non-structural provisions:

The provisions are much more complicated.
The provisions are much more difficult to understand.
The provisions can produce nonsensical results.
The provisions contain outright errors.

It is my opinion that SEAOC should work to restore the 1994 UBC provisions.

-Gary

Gary R. Searer, P.E., S.E.  -  gsearer(--nospam--at)wje.com
Wiss, Janney, Elstner Associates, Inc.