Where are your proposed sketches and weights ? Did the agitator vendor give you design loadings ?

Since this is obviously your first time designing this, and you are obviously not an engineer, many details are necessary !!

An experienced structural or mechanical engineer could help you tremendously ...

If this is only 30 inch diameter vessel, why not a reinforced flat top with a hinge ?

Are the liquids dangerous ? radioactive ? corrosive ?

Must the agitator be periodically removed from the tank ?

Is the tank made from metal ?, plastic ? wood ? .... Too many unknowns

NOBODY CAN GIVE YOU A SPREADSHEET THAT WILL FIGURE ALL OF THIS OUT !!!

Let the guessing games begin !!

MJCronin
Sr. Process Engineer

That's a good question.
If it's safety-critical (poisonous, corrosive, hot, etc.), don't take shortcuts, just get an engineer to check into it.
Realistically, as you go down the scale of size and importance and cost, you get to some point where design work simply isn't done.
For example, if you build a "tank" in a chemical plant, it'll be analyzed for pressure, for wind, for seismic, etc.
But if you have a 55 gallon drum there in the same plant, nobody checks it for wind, for seismic, etc.
So at a 30-inch size, you're pretty close to that 55 gallon drum.
If the vessel is very thin-wall, it may be possible to mount the agitator independently of the vessel.
Normally, equipment like the agitator would tell you the weight and forces associated with the equipment, and also what stiffness was required in the supports. (The stiffness itself isn't the issue, but that's how they avoid vibration problems.)

@MJCronin and JStephen, thank you for your insight. My intention was to learn about any formulas, or literature or software for this type of calculation so that I could do it by myself.
That's the reason why I didn't provide any detailed information. The vessel is a conical open vessel with a 28-inch diameter and 26-inch height made of ss316 with a 1/4-inch thickness. Actually, the thickness is not accurate because we bought it from the auction and the manufacturer lost the information about this vessel. Basically, we are modifying this vessel to meet our specifications because these days, the lead time for new design vessels is too long.
The manufacturer provided me with the weight of the agitator, which can be assumed as axial loading, besides any other loading. The shaft length is around 24 inches, and the thickness is 3/4 inches. Our mixture loaded in the vessel has high viscosity of up to 10000cps. So, due to that high viscosity, I am a bit worried about the bending load on the shaft and vibration but I don't think that will be a big issue.
There will be no issue regarding safety. The material of the vessel is ss316. The material thickness is around 1/4 inch.
I consider mounting the agitator independently or putting the agitator on the bridge or plates over the open vessel. I want to know any literature or formula to determine whether the vessel can withstand that weight. I heard that normally, we don't worry about this thing with this small vessel but I want to make this a learning opportunity for future bigger vessel design instead of just assuming everything will be okay.

This is quite a complex thing so not a simple spreadsheet.

Fixing the agitator to the vessel will add torsional load to the vessel which could be significant depending where the vessel is fixed to the ground.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

1) You mention pressure so that means this is a sealed agitator. Do not mount the agitator to a separate structure unless it is rigidly connected to the tank nozzle and all loads, deflections, and stresses have been evaluated.

In other words, the mixer and its structure see loads and will deflect. If the mixer is not fully supported by the tank nozzle, the vessel will deflect independently from the mixer and just a .015 inch radial movement between the two can fail the mechanical seal or stuffing box.

2) Ultra high viscosity fluids tend to have low instability forces at the impellers, which is helpful. That said, there should be radial forces or a total bending moment from the agitator supplier. Torque is relevant. Weight is relevant. Rule of thumb to ensure the mixer is adequately supported: combine all of the mixer loads and ensure the mounting nozzle will not deflect more than .03" in any direction and angularly deflect more than .12 degrees from the bending moment. 0.25 degrees if you feel less conservative. These loads should be in the agitator documentation. That should take care of the agitator.
Now for the vessel, apply the same loads to the tank nozzle plus the other normal vessel loads and evaluate stress against the appropriate vessel code.
At 10000cP, your fluid is stubborn and don't be surprised if your home-made combination has dead zones or inefficient mixing. The right mixer and vessel design will outperform random mixing impellers by orders of magnitude. (This is much less of an issue when mixing water-like fluids)

3) MJCronin brought up a number of reasons why you might want to offload this exercise. I expect you can get a new agitator, designed for high viscosity mixing, and get the existing vessel re-analyzed by a consultant.

Overall I agree there is no spreadsheet (that anyone is willing to share) to cover all or even a few of the possible scenarios. It takes some work.