API 650 Figure E-1 (Ci Coefficient)

[Andy42]

I am working on a tank calculation for FRP vessels and using API 650 as a guide to develop the sloshing calculations. The graph provided in Figure E-1 (Ci coefficient) seems to limit out at 1.5 (H/D) ratio. Has anyone out there had experience in what to do when the magical 1.5 H/D ratio is exceeded?
Much obliged!

 

[JStephen]

For a "normal" tank, the tank shell is assumed to be rigid, contents are assumed to slosh, and calculations made accordingly.

If desired, calculations can be made assuming the shell is not rigid, and in that case, Fig. E-1 can be used to calculate the fundamental period of the tank shell. I believe Figure E-1 is based on a steel tank, and is an approximation made by evaluating Veletsos' method over a range of parameters, and that method could be used directly instead of using the Ci graph (be aware that it's kind of a mess). This would normally be applicable for either very large tanks or tanks in very high seismic loading, where the extra analysis is worthwhile.

For a (presumably) small FRP tank, I would use the standard method and skip the Ci calculation altogether.

For larger tanks, the consideration of sloshing results in additional freeboard required, but a decrease in overturning moment. ASCE 7 allows you to consider small tanks as entirely rigid, which would be another approach to look into.

 

[Andy42]

Thank you very much for the quick reply. Unfortunately, our tanks have can range from 10' diameter x 60' tall to 100' diameter x 75' tall. We make a number of smaller "shop fabricated" tanks too but I am attempting to write this calculation to cover all aspect ratios. I will look into Veletsos' method, but am afraid that a rigid assumption would not be appropriate for most of what we build.
Much obliged!