I'm not sure I entirely understand the question, so if I miss the point, pardon that.
The ground moves back and forth laterally. Due to friction with the ground, the tank is also forced to move with the ground. Due to inertia, the tank and tank contents above the base resist this motion, which is seen as a net overturning moment about the base of the tank. This results in alternating compression on one side of the tank and in uplift on the other side. If severe enough, this uplift is resisted by anchor bolts.
Force in the bolt itself is calculated via the procedures in API-650.
Design of the bolt embedment in the concrete is addressed in ACI-318.
Design of the anchor chair side plates, anchor chair top plates, and tank shell in the immediate vicinity of the anchor chair is checked via the procedures in the AISI book referenced in API-650.
Compression on the other side of the tank is addressed in separate design checks spelled out in API-650.
Seismic forces also cause increased hoop stress in the tank shell, and API-650 includes equations for that.
Seismic action may require increased freeboard to keep the sloshing wave from damaging the roof, and API-650 includes design checks for that.
Lateral acceleration may also affect the tank roof structure, and requirements for seismic design of the roof structure may vary.
Movement of the tank may damage attached piping, so there are requirements for pipe flexibility.
The ground also moves up and down while moving laterally, and this can increase the compression loading, and reduce the uplift resistance, and this is also addressed in API-650.
On the "every component"- there are design checks for specific areas that are known to have been problems. So not necessarily every component is analyzed.
The seismic loads are calculated assuming 100% elastic action, then reduced by an R factor to allow for increased period and increased damping due to non-elastic effects. So don't get too hung up on calculating stresses to 8 decimal points when that R factor could be +/- 50% or more. Similarly, the seismic factors used for design could have a good bit of uncertainty built in.
There are some youtube videos showing seismic sloshing in swimming pools that are informative. In particular, all the seismic design is assuming forces from any one direction, while the actual earthquake is happening in all directions at once.

JStephen - an impressive answer!

This research paper on Storage Tank Anchor chairs might help ...

http://www.astanks.com/Statii/S_EN/UACEG_Anchors_c...

I believe that your MBA boss may have given you (an obvious newbie) vague and poor direction ...

There are other threads on eng-tips that discuss tank anchor chair designs and the pros and cons of each

Please be a responsible eng-tip member and share some of your conclusions, research and recommendations !

Thank You

MJCronin
Sr. Process Engineer

Why not mention the wind?
Wind can be more dangerous than seismic.

Regards

JStephen thank you so much for the guidance, it was really helpful. Figured out most of my task with what you gave me. I was trying to understand more about how to derive and analyze everything from scratch, as if starting from a blank slate. I guess a lot of it is based on estimations, some of the content and assumptions don't make much sense and i'm hoping it's built on some statistics or experience that isn't being mentioned.
I'd have liked to find some commentary or a committee member giving some insight on these.

MJCronin, yes it was extremely vague but it pushed me into the research so i'm not complaining. Thank you for the paper! And as far as sharing my conclusion goes, I don't believe I have enough experience to be able to formulate something that is useful just yet. Thank you for the help.

r6155, yes i'm well aware but i was tasked with seismic so that's what i'm on right now

For compression plate and gusset plates see a guide in "Process Equipment Design" by Brownell $ Young, support for vertical vessel.

Regards