Periodic time for empty tank for seismic analysis

[DSB123]

API 650 gives equations for the periodic times for the impulsive and convective components of a liquid filled tank as the tank is not the governing component. However API 650 does not give the equations for an empty tank. Does anyone know where equations may be found for this case. Example outer tank of a single containment tank?

 

[JStephen]

Generally, tanks aren't even checked for seismic loading when empty, which is why you don't find much information on the topic. The simplest solution would be to treat the tank as "rigid", which would just involve omitting the liquid terms from the different API equations. You could also calculate an impulsive period for an empty tank by treating it as a cantilever beam fixed at the base, and applying Rayleigh's or Rayleigh/Ritz method, etc. (For many tanks, shear deflection in the shell will be significant and should not be neglected.)