I am not familiar with this type of constaruction but IMO best to follow the advice of the engineeer and architect or maybe live to regret it. I think saving money on the actul support of your home is not ideal

I dont know anything about the piers, but, 2 feet is awfully low for a crawl space. I would increase the size of that. A higher crawl space makes working on anything under the house a whole lot easier.

As specified or larger. Assuming you're DIY look carefully at the engineered detail. The "footing" is the portion that bears on the ground or in the hole. Only need a form for portion above the hole IF required. I don't build in TX. Do they allow prefab pier blocks set in the footing to use wood posts to connect to beams? Look for detail. You'll see this as well as concete if you google "pier and beam foundation"

Any questions ask the architect.

If you have an engineer and an architect you already have the expertise needed to answer this question. They did the load calculation, random people on the interweb did not. You can be sure that if it doesn't match your drawings the inspecotr will red tag it and you'll be starting over.

Note for load capacity it's usually the bottom of the foot they care about, not the part that extends up to the structure, hence the common use of "bell bottom" forms for piers. You have to dig bigger holes to install them, but they use less concrete.

I suspect if you don't go with the architect's spec, and you've submitted framing plans to the city for your permit based on the 12" posts, it won't pass inspection if the framing material is different than specified.

If the engineer signed off on 12", then your options would be to ask then if 10" would work, and/or how many more 10" would be necessary to support the load of the 12", or use the 12".

Thank you all for your answers. I think you are spot on, Patricia -- reading that was extremely convincing. I do want a crawl space for plumbing and electrical -- I've owned both slab and pier and beam and prefer the latter considerably. There's no inspection, no engineer, no architect except for plans that were engineer stamped bought online. The architect originally planned it with 16" piers 4'2" apart, which struck me as absurd, and he said 12" would work. I could ask him about 10", but I think, finally, it's best to spend the money, stop thinking about it, and sleep a bit better.

This is a true DIY project with financial constraints being done by a moderately capable DIY'er. So again, thank you all, I have not heard any ideas outside of those rattling about in my own brain and I was going a bit loopy thinking about this phase, regarding which I have absolutely no experience.

You paid for the math; use it please.

"There's no inspection, no engineer, no architect except for plans that were engineer stamped bought online."

The engineer's stamp on plans bought online is worthless. The sizing of a foundation should be based upon the weight of the structure and the bearing capacity of the soil. The engineer that sealed the drawings knows only half the information needed at best. Get a local engineer to answer your question.

STOP right now I have no clue where you live but IMO no inspection needed is a huge red flag for any DIYer . Who could possibly sign off on a set of plans off the internet. Codes are very specific to where you live and they are there to prtct you and your others. We had a guy where we lived who decided he could roneovate hs home DIY (what could be so hard ) well he removed a laod bearing wall we had ahuge snow storm and his roof caved in so much for easy .

Oh please. Millions of structures around the world have been built by non-pros, were never inspected by anyone, and are still standing and serving their purpose a hundred and more years later. Some I've built are still doing just fine at least 50 years later. About 50% of the standing housing stock in our town predates codes and inspectons. Most of them are much better done than the more recent ones. The blanket presumption that codes and inspections are some sort of universal panacea is belied by just going to look at "modern" buildings, built to code and fully inspected, that have failed in storms or that are put together in a way that they will rot and become uninhabitable in a few decades. There are a vast number of things essential to a good building that are not in the code and that no inspector will ever look for.

To be clear, I follow (usually well exceed) code requirements and always obtain all permits and inspections that are required. But code requirements are a bare minimum.

In the OPs case, I'm guessing s/he is early in the learning process. Clearly you can't size footers without knowing your soil type and condition. The codes don't really help you with that and it is the rare inspector who will be that familiar with local soil conditions in every part of their local jurisdiction; no inspector I've ever worked with would tell you what you need to do-- they look for the specification from the foundation designer who, one hopes, has inspected the site in person and done any testing necessary. Agree completely that a plan off the interweb won't cut it unless it's ridiculously over-spec'd.

DIY construction can and very frequently is well designed and well done; many of us DIY because we want a better product than we can get from a pro-- they simply can't afford to spend the amount of time on things that I might. It takes serious study and practice, willingness to rip things out and try again if you don't get it right the first time, and willingness to admit when you really do need a pro (I'm never going to be good enough at plastering walls).

Back to the op's questions @Doug McCauley

Get specific with the engineer. Do the above portion of the piers need to be concrete? or is it the portion below ground only (bearing)? There is a difference between the soil bearing portion and the portion from the ground to the beams. Its possible this can be done with wood posts which is typical many places.

Saving money on the foundation of your house is the worst idea possible. No one on this forum can answer your question. You say an architect and engineer have "approved" your plans. Listen to them, not us. And find another place to save money if you need to.

If you purchased a set of stock plans designed by an architect and/or structural engineer they are designed to meet a particular building code and particular, site-specific conditions--both of which may be very different from those in your locale. The design of your pier footings will be based on the load, the bearing capacity of the soil, and the frost depth. If you want to optimize the design of the footings and piers, I suggest you consult with a professional engineer licensed to practice in your state.

Doug - Do you like to gamble?