I am new to the forum so forgive my ignorance if this matter has already been discussed at length elsewhere.
I'm evaluating a vertical atmospheric storage tank to determine the minimum required thickness for all shell courses. The tank is 97' tall and is constructed of A283-C carbon steel. The bottom shell course is 26' in diameter, the upper shell is 45' in diameter. There is a conical section in between and the half-apex angle is 30 degrees. API 650 does not cover conical sections. API 620 and ASME Section VIII do however and these are the codes I referred to in an effort to determine the minimum allowable thickness of the cone.
The formulas for calculating t-min on a conical section in both API 620 and ASME Section VIII Div 1 are different, but yield similar values. The concern I have is that I am ending up with a t-min value that is not conservative enough. It seems that I should considering the added stress imposed on the cone by the mass of the fluid resting on it (in addition to the hydrostatic load).
For example: Let's assume that two vessels are designed with a conical section. One vessel has only pressurized air inside and the other has only water and is vented to the atmosphere. The goal is to determine t-min at a point on the cone of both vessels. If the pressure acting on the cone is exactly the same (at a point) the the formulas provided in the ASME and API codes will determine that the t-min is the same for both vessels. The weight of the gas is negligible, but the weight of the fluid is certainly not negligible. Why doesn't the cone of the vessel with water inside require a greater minimum wall thickness? The t-min value would be the same if the shell was vertical for both vessels (that makes sense because a vertical wall has no horizontal component that can carry the vertical load of the water).
The ASME and API codes apply the cosine of the half-apex angle to the denominator of the t-min equations. As the angle increases, the cosine value obviously decreases to zero. This means that as the angle increases, so does the stress in the cone. I have wondered if using the cosine of the half-apex angle in the denominator is a simplified way to increase the stress value in the cone and it is so conservative that it can be applied to without having to consider any moments imparted by the weight of the fluid above.
Perhaps I'm missing some basic engineering principle that would make everything more clear. Any input would be greatly appreciated!