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Seismic Design of Elevated Silo Framing

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Rich, first of all you don't want to be using methodology meant for
liquid storage tanks. Dividing tank silo loads into impulsive and
convective components only applies to liquids. Silos full of sand only
have impulsive forces. Convective periods relate to the sloshing
component of accelerated liquids. It sounds like you are new to tank
design standards. It's a little confusing at first.

Look at ASCE 7-05 section 15.3.2 for starters, since the silos will
undoubtedly weigh more than 25% of the total structure. Treat the silos
filled with sand as if they were rigid, which won't be too far off, and
model as described in paragraph 1. ASCE-7 allows you to use the R value
for the framing system, but if you wanted to be more prudent, I would go
to a reference like AWWA D100 and check the recommended R value for
impulsive loads for ground supported or elevated tanks and use the
lowest of all the R values. A very flexible support framing system is
not what you want, since the tanks will wave all over the place under
seismic loads. I would use braced frames on each side and not consider
moment frames if you can help it.

If you are using modeling software, after you set up your frame model,
you can model the effects of each silo's mass by creating a point at
each silo center of gravity, and then "locking" them to their
appropriate connection points. The vertical location of these points
will vary with the assumed fill depth for each silo. Apply silo weight
and seismic loads at the center of gravity points, and the frame model
will distribute them. You can get away with this because the tanks are
essentially rigid compared to the frame, especially when full of sand.

You could probably get some peculiar effects depending on which tanks
are full and which are empty. Orthogonal load effects are significant in
a structure like this, so you will need to consider a lot of potential
load combinations. One of the complexities in this sort of problem is
that the tanks may not vibrate in phase, since their natural periods
will change depending on how full they are. I would not normally get
into that level of analysis, but it's something to consider. To model
those sorts of effects, you would need to make your model a lot more
complicated, and I doubt your client is interested in paying you to do
that. The braced frame approach is a good one. You will also want good
bracing of the platform, which is a challenge with silos because the
usual location for horizontal bracing elements will probably conflict
with the funnel location.

If you have to design the silos themselves, there are other issues, but
it doesn't sound like that is part of your problem.



Jim Lutz, PE, SE
Senior Structural Engineer
BHC Consultants, LLC


1601 5th Avenue, Suite 500
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>From digest Oct 8, 2010
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From: <SEAInt05(--nospam--at)lewisengineering.com>
To: <seaint(--nospam--at)seaint.org>
Subject: SEISMICE DESIGN OF ELEVATED SILO FRAMING

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I working on the seismic design of a steel frame support structure for
silos.  It will have 6 silos, 12 feet diameter and 38 feet tall.  Sand
is
stored in the silos.  I am using ASCE 7-05 and NEHRP.  I am also using
API
650 and AWWA D100 as a reference.  I am using concentrically braced
frames
for lateral stability.

 

I'm struggling to find determine the seismic forces.  Sometimes I'm a
slow
learner and need good examples to understand technical documents.  I
can't
find good examples for elevated silos or tanks.  I know Harold helped
write
the EXAMPLES chapter 12 for the NEHRP provisions.  Unfortunately, the
examples for silos or tanks are for ground supported ones, not elevated
ones.  Perhaps he can expand on it with this post.

 

As I see it, I have two seismic forces.  The first is impulsive and the
second is convective.   The NEHRP example refers to AWWA D100 for some
design information.  It appears to me that the live load weight in the
silos
is broken down into 2 categories, one is impulsive weight and the other
is
convective weight.  The 2 add up to 100% of the total live load.
Apparently
the chart for this breakdown is in AWWA D100 Commentary, Fig A.5 and the
API
650 Commentary, Fig E6-8.  It would be nice if this was included in ASCE
7
or NEHRP.  Instead I had to spend big bucks for the two standards..  But
I
digress.  The charts calls this a liquid ratio.  I am assuming that this
will also work for sand.  Is that a correct assumption?

 

ASCE 7 says you can't estimate the fundamental period with the equations
from section 12.8.2.1.  They must be calculated.  Here is a challenge
for me
since I just haven't had to do this before.  To get the fundamental
period
of a 3 bay braced frame I started out with determining the stiffness of
the
assembly.  I created a plane frame of the braced system, through 10 kips
horizontal on the system, analyzed and printed out the horizontal
displacement.  I calculated the stiffness K = FORCE/DISPLACEMENT.  I
then
calculated the natural frequency from OMEGA = SQRT(g*K/W).  For W I used
the
dead weight of the frame + tank and the live load of the product.  I
then
calculated the fundamental period T = 2*PI/OMEGA.  Is this the right
approach?

 

I then stepped through the rest of the calculations to determine the
impulsive seismic shear.

 

Next came convective calculations.  First, what is the convective
period?
ASCE 7 15.7.6.1 has an equation in the ground supported tank section.
This
same equation is mentioned in the ground supported tanks section of AWWA
and
API, but no mention of it in the elevated tank section, except a
statement
that it is to be greater than 3 times period T .  After much searching
it
dawned on me that maybe the convective period is just related to a tank
and
is independent of whether it is ground supported or elevated.  So I used
the
ground support equation to calculate the convective period.  Was that a
correct assumption?  Convective is based on sloshing.  The equation for
the
period does not have anything in it related to the material being
sloshed.
API 650 is for petroleum and AWWA D100 is for water.  The period
equations
are the same.  Is it okay to use this same equation for a granular
material
such as sand?  I would think the wave of the slosh would be smaller with
sand than with water.  

 

Again, the elevate tank section of ASCE 7 does not have the equations to
calculate the convective base shear, like the ground supported section.
I
used the same equations as the ground supported section ASCE 7 Eq
15.7-10,
11, 12, to get the convection base shear.  Was this the right approach?

 

To sum it up, I then added the impulsive and convective base shears to
get a
total base shear for by braced frame system.  Fortunately I did all this
in
MathCAD so I can make quick modifications.  So where might I have to
revise
this approach.

 

While I'm on my soap box, here is another wish list item I have.  I wish
someone would write a paper or tutorial on how to use a typical frame
analysis program to do a dynamic analysis like an seismic analysis.
Again,
I like set-by-step procedures that explain what to do and why it is
being
done, what information is needed, and what does the output actually tell
me.
I have several books on structural dynamics and I thumb through and see
all
the matrix equations and spectral response curves, but not practical
step-by-step procedure needed for real-world application with a common
frame
analysis program.  I typically use RAM Elements for my analysis, but I
have
experience using several other packages.  If anyone knows of any
published
papers on the Internet or books to purchase please let me know about
them.

 

Look forward to seeing some of the responses.  Thanks for your help.

 

Rich


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