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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  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 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.